chapter 2 physics
A fireman, 57.6 m away from a burning building, directs a stream of water from a fire hose at an angle of 35.2° above the horizontal. If the initial speed of the stream is 42.7 m/s, at what height will the stream of water strike the building?
27.3 m
Gwen releases a rock at rest from the top of a 40-m tower. If g = 9.8 m/s2 and air resistance is negligible, what is the speed of the rock as it hits the ground?
28 m/s
Wiley Coyote has missed the elusive road runner once again. This time, he leaves the edge of the cliff at 52.4 m/s horizontal velocity. If the canyon is 140 m deep, how far from his starting point at the edge of the cliff does the coyote land?
280 m
When a drag strip vehicle reaches a velocity of 65.0 m/s, it begins a negative acceleration by releasing a drag chute and applying its brakes. While reducing its velocity back to zero, its acceleration along a straight-line path is a constant −7.10 m/s2. What displacement does it undergo during this deceleration period?
298 m
An object, initially moving in the negative x-direction, is subjected to a change in velocity in the positive y-direction. If the resulting velocity vector is drawn from the origin, into which quadrant does this vector point?
2nd
A speeding car traveling at a constant velocity of v passes a police car initially at rest beside the roadway. If the police car with constant acceleration of a immediately pursues the speeding car, how long is it before the police car is directly behind the speeding car?
2v/a
Amanda is standing at the edge of a cliff. She throws a rock vertically upward at speed v0, while at the same time throws a second rock vertically downward at the same speed. How long after the rock thrown downward hits the ground does the rock thrown upwards hit?
2v0/g
A bird, accelerating from rest at a constant rate, experiences a displacement of 25 m in 15 s. What is the final velocity after 15 s?
3.3 m/s
A rock is thrown straight up with an initial velocity of 17.6 m/s. What time interval elapses between the rock's being thrown and its return to the original launch point? (Acceleration due to gravity is 9.80 m/s2.)
3.60 s
Omar throws a rock down with speed 12.5 m/s from the top of a tower. The rock hits the ground after 1.50 s. What is the height of the tower? (air resistance is negligible)
30.0 m
A rock is thrown straight up with an initial velocity of 25.0 m/s. What maximum height will the rock reach before starting to fall downward? (Take acceleration due to gravity as 9.80 m/s2.)
31.9 m
A quarterback takes the ball from the line of scrimmage, runs backward for 12 yards, then sideways parallel to the line of scrimmage for 18 yards. He then throws a 47-yard forward pass straight downfield perpendicular to the line of scrimmage. The receiver is tackled immediately. How far is the football displaced from its original position?
39 yards
Plane A is flying at 440 mph in the northeast direction relative to the Earth. Plane B is flying at 550 mph in the north direction relative to the Earth. What is the speed of Plane B as observed from Plane A?
392 mph
Maria throws two stones from the top edge of a building with a speed of 22 m/s. She throws one straight down and the other straight up. The first one hits the street in a time t1. How much later is it before the second stone hits?
4.5s
A river flows due east at 2.0 m/s. A boat crosses the 300-m-wide river by maintaining a constant velocity of 15 m/s due north relative to the water. If no correction is made for the current, how far downstream does the boat move by the time it reaches the far shore?
40 m
Plane A is flying at 350 mph in the northeast direction relative to the Earth. Plane B is flying at 460 mph in the north direction relative to the Earth. What is the direction of motion of Plane B as observed from Plane A?
40.7° N of W
A stone is thrown at an angle of 30° above the horizontal from the top edge of a cliff with an initial speed of 8.0 m/s. A stopwatch measures the stone's trajectory time from top of cliff to bottom to be 5.9 s. How far out from the cliff's edge does the stone travel horizontally? (g = 9.8 m/s2 and air resistance is negligible)
41 m
A rock is thrown straight down with an initial velocity of 14.3 m/s from a cliff. What is the rock's displacement after 2.0 s? (Acceleration due to gravity is 9.80 m/s2.)
48 m
A projectile is fired directly upwards at 49.4 m/s. A second projectile is dropped from rest at some higher elevation at the instant the first projectile is fired and passes the first projectile 3.00 s later. From the frame of reference of the first projectile, what is the velocity of the second projectile as it passes by?
49.4 m/s downward
A cart is given an initial velocity of 5.0 m/s and experiences a constant acceleration of 2.4 m/s2. What is the magnitude of the cart's displacement during the first 5.0 s of its motion?
55 m
A ball is launched from ground level at 25 m/s at an angle of 31° above the horizontal. How far does it go before it is at ground level again?
56 m
A jet airliner moving at 470 mph due east moves into a region where the wind is blowing at 110 mph in a direction 30.0° north of east. What is the new velocity and direction of the aircraft?
568 mph, 5.56° N of E
Superguy is flying at treetop level near Paris when he sees the Eiffel Tower elevator start to fall (the cable snapped). His x-ray vision tells him Lois LaTour is inside. If Superguy is 1.00 km away from the tower, and the elevator falls from a height of 230 m, how long does Superguy have to save Lois, and what must be his average speed?
6.85 s, 150 m/s
A drag racer starts from rest and accelerates at 8.0 m/s2 for the entire distance of 300 m. What is the velocity of the race car at the end of the run?
69 m/s
A helicopter is traveling at 50.0 m/s at a constant altitude of 150 m over a level field. If a wheel falls off the helicopter, with what speed will it hit the ground? (g = 9.8 m/s2 and air resistance negligible)
74 m/s
A railroad train travels forward along a straight track at 90.0 m/s for 1 000 m and then travels at 70.0 m/s for the next 1 000 m. What is the average velocity?
78.8 m/s
A cheetah can maintain its maximum speed of 96.0 km/hr for 26.0 seconds. What minimum distance must a gazelle running 85.0 km/hr be ahead of the cheetah to escape?
79 m
A rifle is aimed horizontally toward the center of a target 120 m away. If the bullet strikes 11.2 cm below the center, what was the velocity of the bullet? (Ignore air friction.)
790 m/s
A cheetah can run at approximately 100 km/h and a gazelle at 80.0 km/h. If both animals are running at full speed, with the gazelle 50.0 m ahead, how long before the cheetah catches its prey?
9.0 s
A projectile is launched with speed v at an angle θ, the angle being less than 45º. What other angle would give the same range for this projectile launched at the same speed v?
90° - θ
A ball rolls down an incline, starting from rest. If the total time it takes to reach the end of the incline is T, how much time has elapsed when it is halfway down the incline?
> 0.5 T
An object moves along the x axis, with its position given by the function x(t) = ½ t3. Which of the following can be obtained from a graph of x vs. t?
All of the above
Two projectiles are launched at 100 m/s, the angle of elevation for the first being 30° and for the second 60°. Which of the following statements is false?
All of the above statements are true
Jeff throws a ball straight up. For which situation is the vertical velocity zero?
At the top
A baseball catcher throws a ball vertically upward and catches it in the same spot when it returns to his mitt. At what point in the ball's path does it experience zero velocity and non-zero acceleration at the same time?
At the top of its trajectory
A baseball is thrown by the center fielder (from shoulder level) to home plate where it is caught (on the fly at an equal shoulder level) by the catcher. At what point is the ball's speed at a minimum? (air resistance is negligible)
At the top of the trajectory
A baseball is thrown by the center fielder (from shoulder level) to home plate where it is caught (on the fly at shoulder level) by the catcher. At what point does the magnitude of the vertical component of velocity have its minimum value? (air resistance is negligible)
At the top of the trajectory
On a position-versus-time graph, the slope of the straight line joining two points on the plotted curve that are separated in time by the interval Δt, is which of the following quantities?
Average velocity
Two objects of different mass are released simultaneously from the top of a 20-m tower and fall to the ground. If air resistance is negligible, which statement best applies?
Both objects hit the ground together
A car is moving along a straight highway and accelerates at a constant rate while going from point A to point B. If the acceleration is positive, increasing the speed of the car, where does the position where the instantaneous speed equals the average speed occur for the interval from A to B?
Closer to A than to B
In a two-dimensional Cartesian coordinate system the x-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function, with respect to the angle between vector and x-axis?
Cosine
In a two-dimensional Cartesian coordinate system the y-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function, with respect to the angle between vector and y-axis?
Cosine
In a two-dimensional Cartesian system, the x-component of a vector is known, and the angle between vector and x-axis is known. Which operation is used to calculate the magnitude of the vector? (taken with respect to the x-component)
Dividing by cosine
A projectile is launched at an angle less than 30° and at speed v. Which will increase the projectile's range more, ignoring atmospheric drag?
Increasing the speed of launch by 50%
A ball of relatively low density is thrown upwards. Because of air resistance the acceleration while traveling upwards is −10.8 m/s2. On its trip downward the resistance is in the opposite direction, and the resulting acceleration is −8.8 m/s2. When the ball reaches the level from which it was thrown, how does its speed compare to that with which it was thrown?
It is less than the original speed upward
An object is dropped from a height. Once it is moving, which of the following statements is true, at least at one point?
Its velocity is never equal to its acceleration
A plane is moving due north, directly towards its destination. Its airspeed is 220 mph. A constant breeze is blowing from west to east at 50 mph. How long will it take for the plane to travel 220 miles north?
More than one hour
A ball is thrown vertically upwards at 19.0 m/s. For its complete trip (up and back down to the starting position), its average velocity is:
Not given
If the displacement of an object is given in SI units by Δx = −3t + 4t 2, at t = 2 s its velocity and acceleration are, respectively:
Positive, positive
A boat moves through the water in a river at a speed of 8 m/s relative to the water. The boat makes a trip downstream and then makes a return trip upstream to the original starting place. Which trip takes longer?
The upstream trip
A baseball is thrown by the center fielder (from shoulder level) to home plate where it is caught (on the fly at shoulder level) by the catcher. At what point is the magnitude of the acceleration at a minimum? (air resistance is negligible)
acceleration is constant during entire trajectory
Which formula is dimensionally consistent with an expression yielding a value for velocity? (a is acceleration, x is distance, and t is time)
at
In the case of constant acceleration, the average velocity equals the instantaneous velocity:
half-way through the time interval.
A strobe photograph shows equally spaced images of a car moving along a straight road. If the time intervals between images is constant, which of the following cannot be positive?
the acceleration of the car
A strobe photograph of a car moving along a straight road shows the interval between each successive image to be diminishing. If the direction of motion of the car is taken as positive, which of the following is/are negative?
the average acceleration of the car
A projectile is launched at an angle θ above the horizontal. Three seconds later the projectile is moving the same angle θ below the horizontal. Which of the following (actual values with units, not just algebraic symbols) can be found from the information given?
the initial vertical component of the projectile's velocity
A projectile is thrown horizontally at 11.5 m/s. The projectile hits the ground 0.570 s later. What is the angle of impact the projectile makes with the horizontal ground?
-25.9°
A car is initially traveling west at 25 mph, and makes a turn north. As the car finishes the turn, its velocity is 20 mph north. It takes 3.5 seconds to complete the turn. What is the average acceleration of the car while it is turning, in mph/s? Let east be the positive-x direction and north be the positive-y direction.
-7.1i + 5.7j
An object moves 10 m east in 30 s and then returns to its starting point taking an additional 50 s. If west is chosen as the positive direction, what is the sign associated with the average velocity of the object?
0 (no sign)
A ball is rolled horizontally off a table with an initial speed of 0.24 m/s. A stop watch measures the ball's trajectory time from table to the floor to be 0.20 s. How far away from the table does the ball land? (g = 9.8 m/s2 and air resistance is negligible)
0.048 m
A bird, accelerating from rest at a constant rate, experiences a displacement of 25 m in 12 s. What is its acceleration?
0.35 m/s2
A ball is rolled horizontally off a table with an initial speed of 0.24 m/s. A stopwatch measures the ball's trajectory time from table to the floor to be 0.36 s. What is the height of the table? (g = 9.8 m/s2 and air resistance is negligible)
0.64 m
A parachutist jumps out of an airplane and accelerates with gravity to a maximum velocity of 68.6 m/s in 7.00 seconds. She then pulls the parachute cord and after a 4.00-second constant deceleration, descends at 10.5 m/s for 60.0 seconds, reaching the ground. From what height did the parachutist jump?
1.03E+3 m
A baseball is released at rest from the top of the Washington Monument. It hits the ground after falling for 5.85 s. What was the height from which the ball was dropped? (g = 9.80 m/s2 and assume air resistance is negligible)
1.68 × 10^2 m
A 50.0-g ball traveling at 22.0 m/s is bounced off a brick wall and rebounds at 21.0 m/s. A high-speed camera records this event. If the ball is in contact with the wall for 2.50 ms, what is the average acceleration of the ball during this time interval?
1.72E+4 m/s2
At the top of a cliff 100 m high, Raoul throws a rock upward with velocity 15.0 m/s. How much later should he drop a second rock from rest so both rocks arrive simultaneously at the bottom of the cliff?
1.78 s
The highest mountain on Mars is Olympus Mons, rising 22 000 meters above the Martian surface. If we were to throw an object horizontally off the mountain top, how long would it take to reach the surface? (Ignore atmospheric drag forces and use gMars = 3.72 m/s2.)
1.8 minutes
A baseball thrown from the outfield is released from shoulder height at an initial velocity of 29.1 m/s at an initial angle of 30.0° with respect to the horizontal. What is the maximum vertical displacement that the ball reaches during its trajectory?
10.8 m
A string attached to an airborne kite is maintained at an angle of 44.0° with the horizontal. If a total of 160 m of string is reeled in while bringing the kite back to the ground, what is the horizontal displacement of the kite in the process? (Assume the kite string doesn't sag.)
115 m
An object moves at a constant velocity of 12 m/s to the southwest for an interval of 20 s. Halfway through this interval, what is the magnitude of its instantaneous velocity?
12 m/s
An object moves at a constant velocity of 12 m/s to the southwest for an interval of 30 s. Halfway through this interval, what is the magnitude of its instantaneous velocity?
12 m/s
A vehicle designed to operate on a drag strip accelerates from zero to 34 m/s while undergoing a straight-line path displacement of 48 m. What is the vehicle's acceleration if its value may be assumed to be constant?
12 m/s2
In which of the following cases is the displacement's magnitude half the distance traveled?
12 steps east followed by 4 steps west
A ball is thrown vertically upwards at 24.5 m/s. For its complete trip (up and back down to the starting position), its average speed is
12.3 m/s.
A bridge that was 10.4 m long has been washed out by the rain several days ago. How fast must a car be going to successfully jump the stream, if we neglect air resistance? Although the road is level on both sides of the bridge, the road on the far side is 3.00 m lower than the road on this side.
13 m/s
A European sports car dealer claims that his product will accelerate at a constant rate from rest to a speed of 100 km/hr in 8.00 s. What is the speed after the first 4.00 s of acceleration? (Hint: First convert the speed to m/s.)
13.9 m/s
John throws a baseball from the outfield from shoulder height, at an initial velocity of 41.5 m/s at an initial angle of 40.0° with respect to the horizontal. The ball is in its trajectory for a total interval of 5.00 s before the third baseman catches it at an equal shoulder-height level. (Assume air resistance negligible.) What is the ball's horizontal displacement?
159 m
Human reaction time is usually about 0.18 s. If your lab partner holds a ruler between your finger and thumb and releases it without warning, how far can you expect the ruler to fall before you catch it? The nearest value is
16 cm
A ball is pushed with an initial velocity of 4.0 m/s. The ball rolls down a hill with a constant acceleration of 1.7 m/s2. The ball reaches the bottom of the hill in 7.0 s. What is the ball's velocity at the bottom of the hill?
16 m/s
A water rocket, launched from the ground, rises vertically with acceleration of 25 m/s2 for 2.0 s when it runs out of "fuel." Disregarding air resistance, how high will the rocket rise?
178 m
A car's initial velocity is 50.0 km/h in the direction 60.0° north of east, and its final velocity is 70.0 km/h in the direction 40.0° south of east. If the time period for this journey is 30.0 minutes, what is the magnitude of the car's average acceleration?
186 km/h/h
An automobile driver puts on the brakes and decelerates from 35.0 m/s to zero in 11.0 s. What distance does the car travel?
193m
A rock is rolled in the sand. It starts at 5.0 m/s, moves in a straight line for a distance of 6.0 m, and then stops. What is the magnitude of the average acceleration?
2.1 m/s2
A bird, accelerating from rest at a constant rate, experiences a displacement of 22 m in 10 s. What is the average velocity?
2.2 m/s
A Cessna aircraft has a lift-off speed of 135 km/h. What minimum constant acceleration does this require if the aircraft is to be airborne after a take-off run of 260 m?
2.70 m/s2
A plane is moving due north, directly towards its destination. Its airspeed is 210 mph. A constant breeze is blowing from west to east at 20.0 mph. At what rate is the plane moving north?
209 mph
A boat moves at 10.8 m/s relative to the water. If the boat is in a river where the current is 2.00 m/s, how long does it take the boat to make a complete round trip of 1 100 m upstream followed by a 1 100-m trip downstream?
211 s
A stone is thrown with an initial speed of 11.5 m/s at an angle of 50.0 above the horizontal from the top of a 30.0-m-tall building. Assume air resistance is negligible, and g = 9.8 m/s2.What is the magnitude of the vertical-velocity component of the rock as it hits the ground?
25.8 m/s
A stone is thrown with an initial speed of 11.5 m/s at an angle of 50.0 above the horizontal from the top of a 30.0-m-tall building. Assume air resistance is negligible, and g = 9.8 m/s2. What is the magnitude of the horizontal displacement of the rock?
26.1 m
A stone is thrown with an initial speed of 11.5 m/s at an angle of 50.0 above the horizontal from the top of a 30.0-m-tall building. Assume air resistance is negligible, and g = 9.8 m/s2.What is the magnitude of the horizontal-velocity component of the rock as it hits the ground?
26.8 m/s
A v vs. t graph is drawn for a ball moving in one direction. The graph starts at the origin and at t = 5 s the acceleration of the ball is zero. We know that at t = 5 s,
the velocity of the ball is not changing.
Consider the magnitude of the average speed, vavg, speed, mag, and the magnitude of the average velocity, vavg, velocity, mag, for the same trip. Which of the following is always true?
vavg, speed, mag ≥ vavg, velocity, mag
A change in a physical quantity w having initial value wi and final value wf is given by which of the following?
wf − wi
Changing the positive direction in a reference frame to the opposite direction does not change the sign of which of the following quantities?
Speed
Which of the following is not a vector quantity?
Temperature
On a velocity-time graph for a particle, suppose the plot starts at some positive velocity and then follows a straight line to zero at a later time. Which of the following must be true about a position vs. time graph for this same time interval?
The curve will rise steeply at first and as time goes on will level out approaching its highest position value at the later time.
Two baseballs are released at the same time. One is dropped from rest and the other is given an initial horizontal velocity. Which of the following is not true? Ignore atmospheric drag.
The horizontal component of velocity increases at a greater rate than the vertical component of velocity for both while they are both in the air.
If a is acceleration, v is velocity, x is position, and t is time, then which equation is not dimensionally correct?
V=a/t
Starting from rest, a car accelerates down a straight road with constant acceleration a1 for a time t1, then the acceleration is changed to a different constant value a2 for an additional time t2. The total elapsed time is t1 + t2. Can the equations of kinematics be used to find the total distance traveled?
Yes, break the problem up into 2 problems, one with the conditions for the first time interval and the other with the conditions for the second time interval, noting that for the second time interval the initial velocity is that from the end of the first time interval. When done, add the distances from each of the time intervals.
A baseball thrown from the outfield is released from shoulder height at an initial velocity of 28.3 m/s at an initial angle of 30.0° with respect to the horizontal. If it is in its trajectory for a total of 4.00 s before being caught by the third baseman at an equal shoulder-height level, what is the ball's net vertical displacement during its 4.00-s trajectory?
Zero
