PHY 1603- Review #1
A commuter airplane starts from an airport and takes the route shown in the figure below. The plane first flies to city A, located 175 km away in a direction 30.0° north of east. Next, it flies for 150 km 20.0° west of north, to city B. Finally, the plane flies 190 km due west, to city C. Find the location of city C relative to the location of the starting point.
Distance= 245 km angle=21.45
When the pilot reverses the propeller in a boat moving south, the boat moves with an acceleration directed north. Assume the acceleration of the boat remains constant in magnitude and direction. What happens to the boat?
It eventually stops and then speeds up in the northward direction.
A jet lands at 15.5 m/s, the pilot applying the brakes 2.08 s after landing. Find the acceleration needed to stop the jet within 5.04 102 m after touchdown.
-0.2546 m/s^2
Can a tangent line to a velocity vs. time graph ever be vertical? Explain. (Select all that apply.) -It would correspond to an infinite instantaneous acceleration. -No. -It would correspond to a negative instantaneous acceleration. -It would correspond to a reasonable positive instantaneous acceleration. -Yes. -It would correspond to zero instantaneous acceleration.
-It would correspond to an infinite instantaneous acceleration. -No.
A baseball is thrown from the outfield toward the catcher. When the ball reaches its highest point, which statement is true -Its velocity is not zero, but its acceleration is zero. -Its velocity and its acceleration are both zero. -Its velocity is perpendicular to its acceleration. -Its acceleration depends on the angle at which the ball was thrown. -None of the above statements are true.
-Its velocity is perpendicular to its acceleration.
A student throws a heavy red ball horizontally from a balcony of a tall building with an initial speed v0. At the same time, a second student drops a lighter blue ball from the same balcony. Neglecting air resistance, which statement is true? -The blue ball reaches the ground first. -The balls reach the ground at the same instant. -The red ball reaches the ground first. -Both balls hit the ground with the same speed. -None of the above statements are true.
-The balls reach the ground at the same instant.
A second hiker follows the same path the first day, but then walks 15.0 km east on the second day before turning and reaching the ranger's tower. How does the second hiker's resultant displacement vector compare with that of the first hiker? List all aspects that apply. (Select all that apply.) -The second hiker's displacement is greater in magnitude. -The two displacements have different directions. -The second hiker's displacement has the same magnitude as the first. -The two displacements have the same direction. -The second hiker's displacement has a smaller magnitude than the first.
-The second hiker's displacement has the same magnitude as the first. -The two displacements have the same direction.
How would the time of the jump and the horizontal distance traveled change if g were changed, for example if the jump could be repeated with the same initial velocity on a different planet? (Select all that apply.) -The time of the jump decreases when g is smaller. -Increasing the time of the jump has no effect on the displacement. -The time of the jump increases when g is smaller. -The displacement increases with increased time of the jump. -The displacement decreases with increased time of the jump.
-The time of the jump increases when g is smaller. -The displacement increases with increased time of the jump.
How does the magnitude of the velocity vector at impact compare with the magnitude of the initial velocity vector? -It is greater at impact. -It is greater initially. -They are the same since the magnitude of the vertical component of velocity is the same at each height on the way up and on the way down. -They are the same since the ball during its flight has an upward acceleration as its height increases and a downward acceleration on its way down.
-They are the same since the magnitude of the vertical component of velocity is the same at each height on the way up and on the way down.
Suppose you are carrying a ball and running at a constant speed, and wish to throw the ball and catch it as it comes back down. Neglecting air resistance, you should do which of the following? -Throw the ball straight up in the air and maintain the same speed. -Throw the ball straight up in the air and slow down to catch it. -Throw the ball at an angle of about 45° with the horizontal and maintain the same speed
-Throw the ball straight up in the air and maintain the same speed.
The graphical solution corresponds to finding the intersection of what two types of curves in the tx-plane? (Select all that apply.) -a straight line sloped downward -a straight horizontal line -a straight line sloped upward -an upward-shaped curve whose slope increases as the displacement x increases -a downward-shaped curve whose slope decreases and then increases as x increases
-a straight line sloped upward -an upward-shaped curve whose slope increases as the displacement x increases
Neglecting air friction effects, what path does the package travel as observed by the pilot? -a straight line sloped downward -a curved path that starts horizontal and then is increasingly bent downward -a vertical line downward -a downward curved path whose tangent line at each point has negative slope -a curved path that is first curved upward and then downward
-a vertical line downward
A tennis player on serve tosses a ball straight up. As the tennis ball travels through the air, its speed does which of the following? -increases then decreases -remains constant -increases -decreases then increases -decreases
-decreases then increases
For the child being pulled forward on the toboggan in the figure below, which of the following is true of the magnitude of the normal force exerted by the ground on the toboggan? -greater than the total weight -possibly greater or less than the total weight, depending on the size of the weight relative to the tension in the rope -less than the total weight -equal to the total weight
-less than the total weight
A tennis player on serve tosses a ball straight up. While the ball is in free fall, its acceleration does which of the following? -increases then decreases -remains constant -increases -decreases then increases -decreases
-remains constant
The speed of a nerve impulse in the human body is about 100 m/s. If you accidentally stub you toe in the dark, estimate the time it takes the nerve impulse to travel to your brain. (Assume that you are approximately 1.80 m tall and that the nerve impulse travels at uniform speed.)
0.018 s
The combined weight of the crate and dolly in the figure is 3.00 102 N. If the man pulls on the rope with a constant force of 20.0 N, what is the acceleration of the system (crate plus dolly), and how far will it move in 2.00 s? Assume the system starts from rest and that there are no friction forces opposing the motion.
0.654 m/s^2 1.31 m
To find the distance traveled by the light beam without using the Pythagorean theorem, you would multiply the distance of 46.0 m by: -sqrt(2) -1 / sin 39.0° -1 / cos 39.0° -sin 39.0° -2 -cos 39.0°
1 / cos 39.0°
A 2.00-m-tall basketball player is standing on the floor 10.0 m from the basket, as in the figure below. If he shoots the ball at a 40.0° angle with the horizontal, at what initial speed must he throw the basketball so that it goes through the hoop without striking the backboard? The height of the basket is 3.05 m.
10.7 m/s
Find the order of magnitude of your age in seconds.
10^9 s
The boat in the figure is heading due north as it crosses a wide river with a velocity of 10.0 km/h relative to the water. The river has a uniform velocity of 5.00 km/h due east. Determine the velocity of the boat with respect to an observer on the riverbank.
11.2 km/h 26.6
The boat in the figure is heading due north as it crosses a wide river with a velocity of 10 km/h relative to the water. The river has a uniform velocity of 5 km/h due east. Determine the velocity of the boat with respect to an observer on the riverbank.
11.2 m/h 26.6 east of north
The best leaper in the animal kingdom is the puma, which can jump to a height of 3.7 m when leaving the ground at an angle of 45°. With what speed must the animal leave the ground to reach that height?
12 m/s
Use the worked example above to help you solve this problem. An astronaut on a space mission lands on a planet with five times the mass and five times the radius of Earth. What is her weight wx on this planet as a multiple of her Earth weight wE?
15 wE
A ball is thrown so that its initial vertical and horizontal components of velocity are 40 m/s and 20 m/s, respectively. Use a motion diagram to estimate the ball's total time of flight and the distance it traverses before hitting the ground.
160 m
A ball is thrown so that its initial vertical and horizontal components of velocity are 60 m/s and 15 m/s, respectively. Estimate the maximum height the ball reaches. (Use 10 m/s2 as the acceleration of gravity.)
183.6 m
Use the worked example above to help you solve this problem. A race car starting from rest accelerates at a constant rate of 4.50 m/s2. What is the velocity of the car after it has traveled 1.36 102 ft?
19.32 m/s
A bag of sugar weighs 3.50 lb on Earth. What would it weigh in newtons on the Moon, where the free-fall acceleration is one-sixth that on Earth? Repeat for Saturn, where g is 1.13 times that on Earth.
2.598 N 17.614 N
A ball is thrown vertically upward with a speed of 14.0 m/s. How long does it take the ball to return back to the ground?
2.86 s
A race car starting from rest accelerates at a constant rate of 5.10 m/s2. What is the velocity of the car after it has traveled 1.32x102 ft? (1 ft = 0.3048 m)
20.3 m/s
A jet plane lands with a speed of 91 m/s and can accelerate at a maximum rate of −4.00 m/s2 as it comes to rest. From the instant the plane touches the runway, what is the minimum time needed before it can come to rest?
22.8 s
A volume of rock has a mass roughly three times a similar volume of ice. Suppose one world is made of ice whereas another world with the same radius is made of rock. If g is the acceleration of gravity on the surface of the ice world, what is the approximate acceleration of gravity on the rock world?
3 g
The driver of a truck slams on the brakes when he sees a tree blocking the road. The truck slows down uniformly with acceleration ‐5.3 m/s2 for 4.20 s, making skid marks 59.4 m long that end at the tree. With what speed does the truck then strike the tree?
3.01 m/s
An airboat with mass 2.42x102 kg, including the passenger, has an engine that produces a forward force of Fprop = 9.86x102 N, and a resistive force Fresisst = 1.62x102 N. Find the acceleration of the boat.
3.40 m/s2
A certain corner of a room is selected as the origin of a rectangular coordinate system. A fly is crawling on an adjacent wall at a point having coordinates (1.9, ‐3.0), where the units are meters. Express the location of the fly in polar coordinates.
3.55 m @ ‐57.7
A skier leaves the end of a horizontal ski jump at 27.0 m/s and falls 8.40 m before landing. Neglecting friction, how far horizontally does the skier travel in the air before landing?
35.4 m
A brick is thrown upward from the top of a building at an angle of 20° to the horizontal and with an initial speed of 12 m/s. If the brick is in flight for 3.2 s, how tall is the building?
37 m
A house is 52.0 ft long and 32 ft wide, and has 8.0‐ft‐high ceilings. What is the volume of the interior of the house in cubic meters and cubic centimeters? (1 ft = 0.3048 m
377 m3
A brick is thrown upward from the top of a building at an angle of 15° to the horizontal and with an initial speed of 15 m/s. If the brick is in flight for 3.3 s, how tall is the building?
40.55 m
How long does it take an automobile traveling in the left lane of a highway at 50.0 km/h to overtake (become even with) another car that is traveling in the right lane at 40.0 km/h when the cars' front bumpers are initially 140 m apart?
50.4 s
Use the worked example above to help you solve this problem. A typical jetliner lands at a speed of 157 mi/h and decelerates at the rate of (12.2 mi/h)/s. If the jetliner travels at a constant speed of 157 mi/h for 1.1 s after landing before applying the brakes, what is the total displacement of the jetliner between touchdown on the runway and coming to rest?
521.739 m
A jetliner lands at a speed of 156 mi/h and decelerates at the rate of (11.2 mi/h)/s. If the jetliner travels at a constant speed of 156 mi/h for 1.1 s after landing before applying the brakes, what is the total displacement of the jetliner between touchdown on the runway and coming to rest? (1 mi = 1609 m)
562 m
A long jumper leaves the ground at an angle of 25.0° to the horizontal and at a speed of 9.0 m/s. How far does she jump?
6.33 m
If a car is traveling at a speed of 28.0 m/s, is the driver exceeding the speed limit of 55.0 mi/h?
62.6 mi/h
A cruise ship leaving port travels 65.0 km 45.0° north of west and then 32.0 km at a heading 30.0° north of east. Find the magnitude and direction of the ship's displacement vector.
64.6 km @ 16.40 west of north
A typical jetliner lands at a speed of 1.60 102 mi/h and decelerates at the rate of (10 mi/h)/s. If the plane travels at a constant speed of 1.60 102 mi/h for 1.00 s after landing before applying the brakes, what is the total displacement of the aircraft between touchdown on the runway and coming to rest?
644m
Use the rules for significant figures to find the answer to the addition problem S = 25.4 + 13 + 16.67 + 8.703.
64x10^4
If a car is traveling at a speed of 30.4 m/s, what is its speed in miles per hour?
68 mi/h
Convert 153 mi/h to m/s
68.397 m/s
A certain car is capable of accelerating at a rate of 0.57 m/s2. How long does it take for this car to go from a speed of 50 mi/h to a speed of 59 mi/h?
7.06 s
Mature salmon swim upstream, returning to spawn at their birthplace. During the arduous trip they leap vertically upward over waterfalls as high as 3.49 m. With what minimum speed (in m/s) must a salmon launch itself into the air to clear a 3.49-m waterfall?
8.27 m/s
An astronaut lands on a moon that has one-thirtieth the mass of Earth and one-fourth the radius. Find the weight of the astronaut standing on this moon in terms of his Earth weight wE.
8/15 wE
A man pulls a 51.0 kg box horizontally from rest while exerting a constant horizontal force, displacing the box 3.50 meters in 2.00 seconds. Find the force the man exerts on the box. (Ignore friction.)
89.25 N
While standing atop a building 45.8 m tall, you spot a friend standing on a street corner. Using a protractor and a dangling plumb bob, you find that the angle between the horizontal and the direction to the spot on the sidewalk where your friend is standing is 26.6°. Your eyes are located 1.86 m above the top of the building. How far away from the foot of the building is your friend?
95.2 m
he eye of a hurricane passes over Grand Bahama Island in a direction 60.0° north of west with a speed of 42.0 km/h. Three hours later, the course of the hurricane suddenly shifts due north, and its speed slows to 26.0 km/h. How far from Grand Bahama is the hurricane 4.80 h after it passes over the island?
??
A hiker begins a trip by first walking 24.5 km southeast from her base camp. On the second day she walks 41.0 km in a direction 60.0° north of east, at which point she discovers a forest ranger's tower. (a) Determine the components of the hiker's displacements in the first and second days. (b) Determine the components of the hiker's total displacement for the trip. (c) Find the magnitude and direction of the displacement from base camp.
A= Ax=17.32 km . Ay= -17.32 km . Bx=20.5 km . By=35.51 km B=Rx=37.82km . Ry=18.19 km C= Mag=41.97 km . direction=25.68 north of east
A truck loaded with sand accelerates along a highway. The driving force on the truck remains constant. What happens to the acceleration of the truck as its trailer leaks sand at a constant rate through a hole in its bottom?
It increases at a steady rate
The left side of an equation has dimensions of length and the right side has dimensions of length squared. Can the equation be correct? -Yes, because both sides involve the dimension of length. -No, because the equation is dimensionally inconsistent.
No, because the equation is dimensionally inconsistent.
A racing car starts from rest and reaches a final speed v in a time t. If the acceleration of the car is constant during this time, which of the following statements must be true?
The average speed of the car is v/2
A juggler throws a bowling pin straight up in the air. After the pin leaves his hand and while it is in the air, which statement is true?
The velocity of the pin is in the same direction as its acceleration on the way down.
Repeat the conversion, using the relationship 1.00 m/s = 2.24 mi/h. Why is the answer slightly different? (Select all that apply.) -2.24 mi/h is not a correct conversion factor to three significant figures. -A different conversion factor from minutes to seconds is used in each case. -The units are not the same. -Using the conversion factor fails to keep extra digits until the final answer.
Using the conversion factor fails to keep extra digits until the final answer.
A farm truck moves due east with a constant velocity on a limitless, horizontal stretch of road. A boy riding on the back of the truck throws a can of soda upward and catches the projectile at the same location on the truck bed, but 20 m farther down the road. What is the shape of the can's trajectory as seen by the boy?
a straight line segment upward and then downward
Colonel John P. Stapp, USAF, participated in studying whether a jet pilot could survive emergency ejection. On March 19, 1954, he rode a rocket-propelled sled that moved down a track at a speed of 632 mi/h (see figure below). He and the sled were safely brought to rest in 1.40 s.(a) Determine in SI units the negative acceleration he experienced. (b) Determine in SI units the distance he traveled during this negative acceleration.
a= -202 m/s^2 b= 198 m
A long jumper (see figure) leaves the ground at an angle of 20.0° to the horizontal and at a speed of 11.0 m/s. (a) How long does it take for her to reach maximum height? (b) What is the maximum height? (c) How far does she jump? (Assume her motion is equivalent to that of a particle, disregarding the motion of her arms and legs.) (d) Use the proper equation to find the maximum height she reaches.
a= 0.384s b= .722 m c=7.94 m d= .722 m
A bartender slides a beer mug at 1.1 m/s towards a customer at the end of a frictionless bar that is 1.0 m tall. The customer makes a grab for the mug and misses, and the mug sails off the end of the bar. (a) How far away from the end of the bar does the mug hit the floor? (b) What are the speed and direction of the mug at impact?
a= 0.50 m b= speed=??? drection=+75.541 below the horizontal
Use the worked example above to help you solve this problem. An airboat with mass 4.34 102 kg, including the passenger, has an engine that produces a net horizontal force of 8.08 102 N, after accounting for forces of resistance. (a) Find the acceleration of the airboat. (b) Starting from rest, how long does it take the airboat to reach a speed of 15.0 m/s? (c) After reaching that speed, the pilot turns off the engine and drifts to a stop over a distance of 50.0 meters. Find the resistance force, assuming it's constant.
a= 1.86 m/s^2 b= 8.06 s c=-976.5 N
A 7.9 kg object undergoes an acceleration of 1.6 m/s2. (a) What is the magnitude of the resultant force acting on it? (b) If this same force is applied to a 4.7 kg object, what acceleration is produced?
a= 12.64 N b= 2.69 m/s^2
A man exerts a horizontal force of 121 N on a box with a mass of 40.2 kg. (a) If the box doesn't move, what's the magnitude of the static friction force (in N)? (b) What is the minimum possible value of the coefficient of static friction between the box and the floor? (Assume the box remains stationary.)
a= 121 N b= 0.307
A car traveling at a constant speed of 24.0 m/s passes a trooper hidden behind a billboard, as in the figure. One second after the speeding car passes the billboard, the trooper sets off in chase with a constant acceleration of 3.00 m/s2. (a) How long does it take the trooper to overtake the speeding car? (b) How fast is the trooper going at that time?
a= 16.9s b=50.7 m/s
An Alaskan rescue plane drops a package of emergency rations to stranded hikers, as shown in the figure. The plane is traveling horizontally at 40.0 m/s at a height of 1.00 102 m above the ground. (a) Where does the package strike the ground relative to the point at which it was released? (b) What are the horizontal and vertical components of the velocity of the package just before it hits the ground? (c) Find the angle of the impact.
a= 181 m b= 40.0 m/s -44.3 m/s c= -48
Use the worked example above to help you solve this problem. An Alaskan rescue plane drops a package of emergency rations to stranded hikers, as shown in the figure. The plane is traveling horizontally at 35.0 m/s at a height of 1.35 102 m above the ground. (a) Where does the package strike the ground relative to the point at which it was released? b) What are the horizontal and vertical components of the velocity of the package just before it hits the ground? (c) Find the angle of the impact.
a= 183.7 m b= 35 m/s c= -55.8
A projectile is launched straight up at 60 m/s from a height of 72.5 m, at the edge of a sheer cliff. The projectile falls, just missing the cliff and hitting the ground below. (a) Find the maximum height of the projectile above the point of firing. 183.82 Correct: Your answer is correct. m (b) Find the time it takes to hit the ground at the base of the cliff. (c) Find its velocity at impact.
a= 183.82 m b=13.355 s c= -70.854 m/s
A ball is thrown from the top of a building with an initial velocity of 20.0 m/s straight upward, at an initial height of 50.0 m above the ground. The ball just misses the edge of the roof on its way down, as shown in the figure. Determine (a) the time needed for the ball to reach its maximum height, (b) the maximum height, (c) the time needed for the ball to return to the height from which it was thrown and the velocity of the ball at that instant, (d) the time needed for the ball to reach the ground, and (e) the velocity and position of the ball at t = 5.00 s. Neglect air drag.
a= 2.04 s b= 20.4 m c= 4.08 s -20.0 m/s d= 5.83 s e= -29.0 m/s -22.5 m
An airboat with mass 3.50 102 kg, including the passenger, has an engine that produces a net horizontal force of 7.70 102 N, after accounting for forces of resistance (see figure). (a) Find the acceleration of the airboat. (b) Starting from rest, how long does it take the airboat to reach a speed of 12.0 m/s? (c) After reaching that speed, the pilot turns off the engine and drifts to a stop over a distance of 50.0 m. Find the resistance force, assuming it's constant.
a= 2.20 m/s^2 b=5.45 s c=-504 N
A ball is thrown from the top of a building with an initial velocity of 24.5 m/s straight upward, at an initial height of 58.8 m above the ground. The ball just misses the edge of the roof on its way down, as shown in the figure. (a) Determine the time needed for the ball to reach its maximum height. (b) Determine the maximum height. (c) Determine the time needed for the ball to return to the height from which it was thrown, and the velocity of the ball at that instant. (d) Determine the time needed for the ball to reach the ground. (e) Determine the velocity and position of the ball at t = 5.62 s.
a= 2.55s b= 30.625 m c= 5s -24.5m/s d=6.88 s e=-30.576 m/s -17.073m
Use the worked example above to help you solve this problem. A car of mass m is on an icy driveway inclined at an angle θ = 15.5°, as shown in the figure. (a) Determine the acceleration of the car, assuming the incline is frictionless. (b) If the length of the driveway is 26.0 m and the car starts from rest at the top, how long does it take to travel to the bottom? (c) What is the car's speed at the bottom?
a= 2.62 m/s^2 b=4.456 s c= 11.67 m/s
A car traveling at a constant speed of 28.1 m/s passes a trooper hidden behind a billboard, as in the figure. One second after the speeding car passes the billboard, the trooper sets off in chase with a constant acceleration of 3.65 m/s2.
a= 20.811 s x= 573.854 m
(a) A car of mass m is on an icy driveway inclined at an angle θ = 20.0°, as in figure (a). Determine the acceleration of the car, assuming the incline is frictionless. (b) If the length of the driveway is 25.0 m and the car starts from rest at the top, how long does it take to travel to the bottom? (c) What is the car's speed at the bottom?
a= 3.35 m/s^2 b= 3.86 s c= 12.9 m/s
(a) Find the polar coordinates corresponding to (x, y) = (3.38, 1.79) m. (b) Find the Cartesian coordinates corresponding to (r, θ) = (3.87 m, 56.2°).
a= 3.82 @ 27.9 b=x=2.15 y=3.216
A grasshopper jumps a horizontal distance of 1.50 m from rest, with an initial velocity at a 47.0° angle with respect to the horizontal. (a) Find the initial speed of the grasshopper. (b) Find the maximum height reached.
a= 3.84 m/s b= 0.402 m
(a) Suppose a hockey puck slides down a frictionless ramp with an acceleration of 4.90 m/s2. What angle does the ramp make with respect to the horizontal? (b) If the ramp has a length of 6.40 m, how long does it take the puck to reach the bottom? (c) Now suppose the mass of the puck is doubled. What's the puck's new acceleration down the ramp?
a= 30 b=1.62 s 4.90 m/s^2
A baseball is hit so that it travels straight upward after being struck by the bat. A fan observes that it takes 3.10 s for the ball to reach its maximum height. (a) Find the ball's initial velocity. (b) Find the height it reaches.
a= 30.83 m/s upward b=47.1 m
a= The Cartesian coordinates of a point in the xy-plane are (x, y) = (-3.4, -2.71) m. Find the polar coordinates of this point. b=Convert (r, θ) = (4.95 m, 36.6°) to rectangular coordinates.
a= 4.30 @216 b= x=3.97 y=2.95
(a) The Cartesian coordinates of a point in the xy-plane are (x, y) = (−3.50 m, −2.50 m), as shown in the figure. Find the polar coordinates of this point. (b) Convert (r, θ) = (5.00 m, 37.0°) to rectangular coordinates. Starting with the answers to part (b), work backwards to recover the given radius and angle. Why are there slight differences from the original quantities? (Select all that apply.) -using inconsistent equations in doing the calculation in both directions -calculator defects -keeping more than three significant figures in intermediate steps of each calculation -rounding the final calculated values of x and y in the example before using them to work backwards
a= 4.30 m @ 216 b= 3.99 m & 3.01 m rounding the final calculated values of x and y in the example before using them to work backwards
Four forces act on an object, given by A = 37.3 N east, B = 41.3 N north, C = 88.7 N west, and D = 62.7 N south. (Assume east and north are directed along the +x-axis and +y-axis, respectively.) HINT (a) What is the magnitude of the net force (in N) on the object? (b) What is the direction of the force? (Enter your answer in degrees counterclockwise from the +x-axis.)
a= 55.68 N b= 203 Counterclockwise from the +x-axis
A car is traveling at 41.0 km/h on a flat highway. (a) If the coefficient of friction between road and tires on a rainy day is 0.113, what is the minimum distance in which the car will stop? (b) What is the stopping distance when the surface is dry and the coefficient of friction is 0.622?
a= 58.6 m b= 10.6 m
A hiker begins a trip by first walking 25.0 km 45.0° south of east from her base camp. On the second day she walks 40.0 km in a direction 60.0° north of east, at which point she discovers a forest ranger's tower. (a) Determine the components of the hiker's displacements in the first and second days. (b) Determine the components of the hiker's total displacement for the trip. (c) Find the magnitude and direction of the displacement from base camp.
a= Ax=17.7 m Ay= -17.7 km Bx=20.0 m By=34.6 km b=Rx=37.7 Ry=16.9 c=24.1
A cruise ship leaving port travels 49.0 km 45.0° north of west and then 67.0 km at a heading 30.0° north of east. (a) Find the components of the ship's displacement vector. (b) Find the displacement vector's magnitude and direction.
a= Rx=23.346 . Ry=68.148 b= Mag=72.036 . Direction=71.090 north of east
Suppose the driver in this example is now moving with speed 37.5 m/s, and slams on the brakes, stopping the car in 3.5 s. (a) Find the acceleration assuming the acceleration is constant. (b) Find the distance the car travels, assuming the acceleration is constant. (c) Find the average velocity.
a=-10.71 m/s^2 b=65.65 m c=18.76 m/s
A farm truck moves due east with a constant velocity of 7.80 m/s on a limitless, horizontal stretch of road. A boy riding on the back of the truck throws a can of soda upward (see figure below) and catches the projectile at the same location on the truck bed, but 11.0 m farther down the road. (a) In the frame of reference of the truck, at what angle to the vertical does the boy throw the can? b) What is the initial speed of the can relative to the truck? (c) What is the shape of the can's trajectory as seen by the boy? -a straight line segment upward and then downward -a symmetric section of a parabola opening downward An observer on the ground watches the boy throw the can and catch it. (d) In this observer's frame of reference, describe the shape of the can's path. -a straight line segment upward and then downward -a symmetric section of a parabola opening downward (e) In this observer's frame of reference, determine the initial velocity of the can.
a=0 b=6.9 c= a straight line d=a symmetric section of a parabola opening downward e= 10.42 m/ 41.53 above the horizontal eastward line
Use the worked example above to help you solve this problem. A long jumper (as shown in the figure) leaves the ground at an angle of 17.0° to the horizontal and at a speed of 10.5 m/s. (a) How long does it take for her to reach maximum height? (b) What is the maximum height? (c) How far does she jump? (Assume that her motion is equivalent to that of a particle, disregarding the motion of her arms and legs.)
a=0.313 s b= 0.481 m c= 6.29 m
An object with a mass of 1 kg weighs approximately 2 lb. Use this information to estimate the mass of the following objects. (a) a baseball (b) your physics textbook (c) a pickup truck
a=10^-1kg b=10^0 kg c=10^3 kg
(a) A race car starting from rest accelerates at a constant rate of 5.00 m/s2. What is the velocity of the car after it has traveled 1.00 102 ft? (b) How much time has elapsed? (c) Calculate the average velocity two different ways.
a=17.5 m/s b=3.50 s c= v1=8.71 m/s v2=8.75 m/s
A jet plane lands with a speed of 94 m/s and can accelerate at a maximum rate of −4.50 m/s2 as it comes to rest. (a) From the instant the plane touches the runway, what is the minimum time needed before it can come to rest? b) Can this plane land on a small tropical island airport where the runway is 0.800 km long?
a=20.89 s b= no
A person measures the height of a building by walking out a distance of 46.0 m from its base and shining a flashlight beam toward the top. When the beam is elevated at an angle of 39.0° with respect to the horizontal, as shown in the figure, the beam just strikes the top of the building. (a) If the flashlight is held at a height of 2.00 m, find the height of the building. (b) Calculate the length of the light beam.
a=39.3 m b=59.2 m
A ball is thrown vertically upward with a speed of 30.0 m/s. (a) How high does it rise? (b) How long does it take to reach its highest point? (c) How long does the ball take to hit the ground after it reaches its highest point? (d) What is its velocity when it returns to the level from which it started?
a=45.87 m b=3.06 s c=3.06 s d= -30 m/s
A truck covers 40.0 m in 8.40 s while uniformly slowing down to a final velocity of 2.95 m/s. (a) Find the truck's original speed. (b) Find its acceleration.
a=6.5738 b=???
(a) If a person can jump a maximum horizontal distance (by using a 45° projection angle) of 1.18 m on Earth, what would be his maximum range on the Moon, where the free-fall acceleration is g/6 and g = 9.80 m/s2? (b) Repeat for Mars, where the acceleration due to gravity is 0.38g.
a=7.08 b=3.105
The combined weight of the crate and dolly as shown in the figure is 2.70 102 N. If the man pulls on the rope with a constant force of 21.5 N, what is the acceleration of the system (crate plus dolly), and how far will it move in 2.00 s? Assume that the system starts from rest and that there are no friction forces opposing the motion.
accelaeration= 0.78 m/s^2 displacement 1.56 m
As a projectile moves in its parabolic path, the velocity and acceleration vectors are perpendicular to each other at which of the following along the projectile's path? nowhere everywhere at the peak not enough information
at the peak
Consider the following controls in an automobile: gas pedal, brake, steering wheel. Which controls in this list cause an acceleration of the car? (Select all that apply.) brake steering wheel none of these gas pedal
brake steering wheel gas pedal
If an object isn't accelerating, no external force is acting on it. (t or f)
false
If an object isn't moving, no external forces act on it. (t or f)
false
If the net force acting on an object is in the positive x-direction, the object moves only in the positive x-direction. ( t or f)
false
A skateboarder starts from rest and moves down a hill with constant acceleration in a straight line, traveling for 4 s. In a second trial, he starts from rest and moves along the same straight line with the same acceleration for only 8 s. How does his displacement from his starting point in this second trial compare with the first trial?
four times larger
For an angle θ measured from the positive x-axis, the values of sin(θ) and cos(θ) are always which of the following? -greater than −1 and less than 1 -less than or equal to −1 or greater than or equal to 1 -less than −1 -greater than +1 -greater than or equal to −1 and less than or equal to 1
greater than or equal to −1 and less than or equal to 1
A person measures the height of a building by walking out a distance of 43 m from its base and shining a flashlight beam toward the top. When the beam is elevated at an angle of 35.2° with respect to the horizontal, as shown in the figure, the beam just strikes the top of the building. Find the height of the building and the distance the flashlight beam has to travel before it strikes the top of the building. (The flashlight is still 2.00 m above the ground.)
height= 32.3m r=52.6 m
A person walks 13.0° north of east for 4.00 km. How far due north and how far due east would she have to walk to arrive at the same location?
north=0.900 east= 3.89
Which has greater value, a newton of gold on Earth or a newton of gold on the Moon?
on the moon
A certain corner of a room is selected as the origin of a rectangular coordinate system. A fly is crawling on an adjacent wall at a point having coordinates (3.8, 1.5), where the units are meters. Express the location of the fly in polar coordinates.
r=4.08 Degree=21.5
Suppose the river is flowing east at 3 m/s and the boat is traveling south at 4 m/s with respect to the river. Find the speed and direction of the boat relative to Earth.
speed= 5m/s 53 south of east
Use the worked example above to help you solve this problem. A ball is thrown so that its initial vertical and horizontal components of velocity are 60 m/s and 15 m/s, respectively. Use a motion diagram to estimate the ball's total time of flight and the distance it traverses before hitting the ground. (Use 10 m/s2 as the acceleration of gravity.)
time= 12.24 s distance= 183.6 m
A projectile is launched from Earth's surface at a certain initial velocity at an angle above the horizontal, reaching maximum height after time tmax. Another projectile is launched with the same initial velocity and angle from the surface of a planet, where the acceleration of gravity is six times that of Earth. Neglecting air resistance and variations in the acceleration of gravity with height, how long does it take the projectile on that planet to reach its maximum height?
tmax /6
An object can move even when no force acts on it. (t or f)
true
If a single force acts on an object, the object accelerates (t or f)
true
If an object accelerates, a force is acting on it. (t or f)
true
A surveyor measures the distance across a straight river by the following method: Starting directly across from a tree on the opposite bank, he walks x = 102 m along the riverbank to establish a baseline. Then he sights across to the tree. The angle from his baseline to the tree is θ = 39.2°. How wide is the river?
y=82.2m
If the speed of the boat relative to the water is increased, what happens to the angle? θ increases. θ decreases. θ remains the same.
θ decreases.
A baseball player moves in a straight‐line path in order to catch a fly ball hit to the outfield. His velocity as a function of time is shown in the figure below. Find his instantaneous acceleration at point A. (refer to practice exam for graph)
‐3 m/s2
An astronaut on a space mission lands on a planet with three times the mass and twice the radius of Earth. What is her weight wx on this planet as a multiple of her Earth weight wE?
(3/4)We
