Physics Exam 1

A hiker begins a trip by first walking 25.5 km southeast from her base camp. On the second day she walks 39.0 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 = 18.03km Ay = -18.03 km Bx = 19.5km By = 33.77 km (b) Rx = 37.53 km Ry = 15.74 km (c)Magnitude 40.70 km Direction 22.75 km north of east

A jet lands at 41.9 m/s, the pilot applying the brakes 1.99 s after landing. Find the acceleration needed to stop the jet within 5.63 102 m after touchdown.

-1.83

Find the instantaneous accelerations at circled A, circled B, and circled C in Figure (b).

-3 Correct: Your answer is correct. m/s2 circled B 1 Correct: Your answer is correct. m/s2 circled C 0 Correct: Your answer is correct.

A projectile is launched straight up at 54.5 m/s from a height of 76.5 m, at the edge of a sheer cliff. The projectile falls, just missing the cliff and hitting the ground below. Find its velocity at impact.

-66.82

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 increases then decreases remains constant 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 1.70 m tall and that the nerve impulse travels at uniform speed.)

.017 s

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 1.90 m tall and that the nerve impulse travels at uniform speed.)

.019 s

To find the distance traveled by the light beam without using the Pythagorean theorem, you would multiply the distance of 46.0 m by:

1 / cos 39.0°

A certain corner of a room is selected as the origin of a rectangular coordinate system. If a fly is crawling on an adjacent wall at a point having coordinates (1.1, 0.6), where the units are meters, what is the distance of the fly from the corner of the room?

1.253 m

While standing atop a building 54.1 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 26.1°. Your eyes are located 1.91 m above the top of the building. How far away from the foot of the building is your friend?

114 m

While standing atop a building 47.2 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 23.3°. Your eyes are located 1.92 m above the top of the building. How far away from the foot of the building is your friend?

114.06 m

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?

12.04 m/s

A fireman d = 42.0 m away from a burning building directs a stream of water from a ground-level fire hose at an angle of θi = 27.0° above the horizontal as shown in the figure. If the speed of the stream as it leaves the hose is vi = 40.0 m/s, at what height will the stream of water strike the building?

14.6

The eye of a hurricane passes over Grand Bahama Island in a direction 60.0° north of west with a speed of 39.0 km/h. Three hours later, the course of the hurricane suddenly shifts due north, and its speed slows to 27.0 km/h. How far from Grand Bahama is the hurricane 4.10 h after it passes over the island?

143

The 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 4.90 h after it passes over the island?

170.6 km

A race car starting from rest accelerates at a constant rate of 6.40 m/s2. What is the velocity of the car after it has traveled 1.13 102 ft?

21 m/s

A brick is thrown upward from the top of a building at an angle of 25° to the horizontal and with an initial speed of 15 m/s. If the brick is in flight for 3.1 s, how tall is the building?

27.4 m

Two points are given in polar coordinates by (r, θ) = (1.40 m, 50.0°) and (r, θ) = (3.80 m, −30.0°) , respectively. What is the distance between them?

3.814 m

A high fountain of water is located at the center of a circular pool as shown in the figure below. Not wishing to get his feet wet, a student walks around the pool and measures its circumference to be 21.0 m. Next, the student stands at the edge of the pool and uses a protractor to gauge the angle of elevation at the bottom of the fountain to be 55.0°. How high is the fountain?

4.77 The circumference of the fountain is C = 2πr, so the radius is given by the following equation. r=C/(2pi)=(21.0 text( m))/(2pi)=3.342 text( m) Thus, we have the following. tan(55.0deg)=h/r=h/(3.342 text( m)) We can then solve for h. h=\(3.342 text( m)\)tan(55.0deg)=<u>4.77 text( m)</u>

A typical jetliner lands at a speed of 151 mi/h and decelerates at the rate of (10.7 mi/h)/s. If the jetliner travels at a constant speed of 151 mi/h for 1.3 s after landing before applying the brakes, what is the total displacement of the jetliner between touchdown on the runway and coming to rest?

564.05

Δxcoasting + Δxbraking = 71.5 m + 572 m = 644 m By how much would the answer change if the plane coasted for 2.0 s before the pilot applied the brakes?

71.5 m

A cruise ship leaving port travels 54.0 km 45.0° north of west and then 67.0 km at a heading 30.0° north of east. Find the displacement vector's magnitude and direction

Magnitude: 74.4 km Direction: 74.5 km north of east

A cruise ship leaving port travels 51.0 km 45.0° north of west and then 71.0 km at a heading 30.0° north of east. Find the displacement vector's magnitude and direction.

Magnitude: 75.94 km Direction 70.44 km north of east

If something is moving in the positive direction, the acceleration must be .....?

Negative

Can a tangent line to a velocity vs. time graph ever be vertical? Explain. (Select all that apply.) It would correspond to a negative instantaneous acceleration. No. It would correspond to zero instantaneous acceleration. It would correspond to an infinite instantaneous acceleration. It would correspond to a reasonable positive instantaneous acceleration. Yes.

No, it would correspond to an infinite instantaneous acceleration

A ball is thrown straight up in the air. For which situations are both the instantaneous velocity and the acceleration zero? (Select all that apply.) at the top of the flight path halfway up and halfway down on the way up on the way down none of these

None of these

How would the answer to part (b), the maximum height, change if the person throwing the ball jumped upward at the instant he released the ball? The maximum height would remain the same. The maximum height would decrease. The maximum height would increase.

The max. height would increase

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 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 two displacements have different directions. The second hiker's displacement is greater in magnitude.

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. The displacement decreases with increased time of the jump. The time of the jump increases when g is smaller. Increasing the time of the jump has no effect on the displacement. The displacement increases 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.

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 never in the same direction as its acceleration. The acceleration of the pin is zero. The velocity of the pin is opposite its acceleration on the way up. The velocity of the pin is in the same direction as its acceleration on the way up. The velocity of the pin is always in the same direction as its acceleration.

The velocity of the pin is opposite its acceleration on the way up

Neglecting air friction effects, what path does the package travel as observed by the pilot? (see pic in phone) a curved path that starts horizontal and then is increasingly bent downward a downward curved path whose tangent line at each point has negative slope a straight line sloped downward a curved path that is first curved upward and then downward a vertical line downward

a vertical line downward

Suppose the driver in this example is now moving with speed 30.1 m/s, and slams on the brakes, stopping the car in 5.0 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) -6.02 m/s2 b) 75.25 m c) 15.05 m/s

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 9.8 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) .2924 s b) .4189 m c) 5.481 m

A bartender slides a beer mug at 1.6 m/s towards a customer at the end of a frictionless bar that is 1.9 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) (b) What are the speed and direction of the mug at impact? speed m/s direction ° below the horizontal

a) .996 m 6.32 m/s and 75.3 degrees

A farm truck moves due east with a constant velocity of 9.05 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 19.0 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) In this observer's frame of reference, determine the initial velocity of the can. magnitude m/s direction

a) 0 b) 10.3 m/s c) 13.7 m/s d) 48.7

A motorist with an expired license tag travels at a constant speed of 12 m/s down a street, and a policeman on a motorcycle, taking another 4.88 s to finish his donut, gives chase at an acceleration of 2.83 m/s2. a) Find the time required to catch the car. b) Find the distance the trooper travels while overtaking the motorist.

a) 11.95 s b) 202.1 m

An Alaskan rescue plane drops a package of emergency rations to stranded hikers, as shown in the figure. The plane is traveling horizontally at 33.0 m/s at a height of 1.20 102 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) 163.3 m b) 33.0 (horizontal) and -48.5 (vertical) c) -55.7 degrees

A car traveling at a constant speed of 26.7 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 3.07 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) 18.34 s b) 56.30 m/s

A motorist with an expired license tag travels at a constant speed of 20.8 m/s down a street, and a policeman on a motorcycle, taking another 4.22 s to finish his donut, gives chase at an acceleration of 2.56 m/s2. a) Find the time required to catch the car. b) Find the distance the trooper travels while overtaking the motorist.

a) 19.7 s b) 517 m

A certain aircraft has a liftoff speed of 123 km/h. (a) What minimum constant acceleration does the aircraft require if it is to be airborne after a takeoff run of 254 m? (b) How long does it take the aircraft to become airborne?

a) 2.30 m/s2 b) 14.86 s

A ball is thrown from the top of a building with an initial velocity of 23.1 m/s straight upward, at an initial height of 52.9 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 = 5.07 s

a) 2.357 s b) 27.22 m c) 4.714 s and -23.10 m/s d) 6.401 s e) -26.59 m/s -8.837 m

The figure below shows the unusual path of a confused football player. After receiving a kickoff at his own goal, he runs downfield to within inches of a touchdown, then reverses direction and races back until he's tackled at the exact location where he first caught the ball. During this run, what is each of the following? (a) the total distance he travels b) his displacement c) his average velocity in the x direction

a) 200 yd b) 0 yd c) 0 yd

A ball is thrown vertically upward with a speed of 22.0 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) 24.70 m b) 2.245 s c) 2.245 s d) -22 m/s

A grasshopper jumps a horizontal distance of 1.20 m from rest, with an initial velocity at a 48.0° angle with respect to the horizontal. (a) Find the initial speed of the grasshopper. b) Find the maximum height reached.

a) 3.439 ms b) .3332 m

A grasshopper jumps a horizontal distance of 1.50 m from rest, with an initial velocity at a 42.0° angle with respect to the horizontal. (a) Find the initial speed of the grasshopper. (b) Find the maximum height reached.

a) 3.84 ms b) 0.337 m

A graph of position versus time for a certain particle moving along the x-axis is shown in the figure below. Find the average velocity in the following time intervals. (a) 0 to 2.00 s b) 2.00 s to 4.00 s c) 4.00 s to 7.00 s d) 0 to 8.00 s

a) 5 m/s b) -2.5 m/s c) -3.3 m/s d) 0 m/s

The diameter of a sphere is measured to be 5.47 in. (a) Find the radius of the sphere in centimeters. cm (b) Find the surface area of the sphere in square centimeters. cm2 (c) Find the volume of the sphere in cubic centimeters. cm3

a) 6.95 b) 606 c) 1400

A truck covers 40.0 m in 7.70 s while uniformly slowing down to a final velocity of 1.60 m/s. a) Find the truck's original speed. b) Find its acceleration.

a) 8.790 m/s b) -.934 m/s2

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: 21.4 west of north

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 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 44 m from its base and shining a flashlight beam toward the top. When the beam is elevated at an angle of 44.6° 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 = 45.39 r = 61.80

A map suggests that Atlanta is 730 miles in a direction 5.00° north of east from Dallas. The same map shows that Chicago is 560 miles in a direction 21.0° west of north from Atlanta. The figure below shows the location of these three cities. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago.

magnitude: 788 mi direction: 48.1 north of east of Dallas

The Cartesian coordinates of a point in the xy-plane are (x, y) = (-3.3, -2.77) m. Find the polar coordinates of this point.

r= 4.3 Degree: -44.5

Find the polar coordinates corresponding to (x, y) = (3.34, 1.29) m.

r=3.59 Degree: 23.46

Convert (r, θ) = (4.52 m, 37.9°) to rectangular coordinates.

x=3.57 y=2.78

If the speed of the boat relative to the water is increased, what happens to the angle?

θ decreases