Question 1

Newton approximated motion in a circle as a series of linear motions, as in the polygon below.  Assume that the particle moves at constant speed vA from A to B, and at constant speed vB from B to C.
Use this exhibit to answer the following question(s).
- The direction of the change in velocity,  , at point B, is shown by the arrow in
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of 
Newton approximated motion in a circle as...

Question 2

Wiley Coyote has missed the elusive roadrunner once again. This time, he leaves the edge of the cliff at 50.0 m/s horizontal velocity. If the canyon is 100 m deep, how far from the edge of the cliff does the coyote land?

Accepted Answer

The answer of Wiley Coyote has missed the elusive roadrunner...

Question 3

A rifle is aimed horizontally toward the center of a target 0.10 km away, but the bullet strikes 10 cm below the center. Calculate the velocity of the bullet just as it emerges from the rifle.

Accepted Answer

The answer of A rifle is aimed horizontally toward the...

Question 4

Raindrops are falling straight downward. When observed from a car traveling at 55.0 mi/h, the drops streak the side window at an angle of 60.0° with the vertical. Find the speed with which the drops are falling.

Accepted Answer

The answer of Raindrops are falling straight downward. When observed...

Question 5

A hunter wishes to cross a river that is 1.5 km wide and flows with a velocity of 5.0 km/h parallel to its banks. The hunter uses a small powerboat that moves at a maximum speed of 12 km/h with respect to the water. What is the minimum time for crossing?

Accepted Answer

The answer of A hunter wishes to cross a river...

Question 6

A track star in the broad jump goes into the jump at 12 m/s and launches himself at 20° above the horizontal. How long is he in the air before returning to Earth?

Accepted Answer

The answer of A track star in the broad jump...

Question 7

A car is driven 1200 m north at 20.0 m/s and then driven 1600 m east at 25.0 m/s. What is the magnitude of the average velocity for this trip?
A)16.1 m/s
B)22.6 m/s
C)31.3 m/s
D)11.3 m/s
E)62.2 m/s

Accepted Answer

The answer of A car is driven 1200 m north...

Question 8

Newton approximated motion in a circle as a series of linear motions, as in the polygon below.  Assume that the particle moves at constant speed vA from A to B, and at constant speed vB from B to C.
Use this exhibit to answer the following question(s).
-The direction of the acceleration,  , at point B, is shown by the arrow in
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of 
Newton approximated motion in a circle as...

Question 9

A car is driven 1200 m north at 20.0 m/s and then driven 1600 m east at 25.0 m/s. What are the magnitude and direction of the displacement for this trip?
A)1400 m, northeast
B)2000 m, 36.9° north of east
C)2000 m, 53.1° north of east
D)2800 m, 36.9° east of north
E)2800 m, 53.1° east of north

Accepted Answer

The answer of A car is driven 1200 m north...

Question 10

A satellite is in a circular orbit 600 km above the Earth's surface. The acceleration of gravity is 8.21 m/s² at this altitude. The radius of the Earth is 6400 km. Determine the speed of the satellite, and the time to complete one orbit around the Earth.

Accepted Answer

The answer of A satellite is in a circular orbit...

Question 11

A fast duck is flying  mi/h at the same altitude as a slow airplane flying with a velocity of  mi/h. How fast and in what direction is the duck moving relative to the airplane?

Accepted Answer

The answer of A fast duck is flying  mi/h...

Question 12

An artillery shell is fired with an initial velocity of 300 m/s at 55.0° above the horizontal. It explodes on a mountainside 42.0 s after firing. If x is horizontal and y vertical, find the (x, y) coordinates where the shell explodes.

Accepted Answer

The answer of An artillery shell is fired with an...

Question 13

While the gondola is rising at a speed of 2.0 m/s, a passenger in a balloon-supported gondola throws a small ball down at a speed of 5.0 m/s relative to his body. A person who measures the ball's velocity at the instant of release will find that the ball's velocity relative to the ground at that instant is
A)2.0 m/s, up.
B)3.0 m/s, down.
C)3.0 m/s, up.
D)5.0 m/s, down.
E)12.8 m/s, down.

Accepted Answer

The initial velocity of the ball relative to the ground is the vector sum of the velocity of the gondola and the velocity of the ball relative to the gondola. Since the gondola is rising at a speed of 2.0 m/s, the initial velocity of the ball relative to the ground is 5.0 m/s - 2.0 m/s = 3.0 m/s down. Therefore, the correct choice is B.

Question 14

A football is thrown upward at a 30.0° angle to the horizontal. To throw a 40.0-m pass, what must be the initial speed of the ball?

Accepted Answer

The answer of A football is thrown upward at a...

Question 15

Jane plans to fly from Binghampton, New York, to Springfield, Massachusetts, about 280 km due east of Binghampton. She heads due east at 280 km/h for one hour but finds herself at Keene, which is 294 km from Binghampton in a direction 17.8 degrees north of due east. What was the wind velocity?
A)14 km/h, E
B)14 km/h, W
C)14 km/h, N
D)90 km/h, S
E)90 km/h, N

Accepted Answer

The wind caused Jane to deviate from her intended due east path to a path 17.8 degrees north of east. Given she ended up 294 km away in this direction after 1 hour, the wind's effect is perpendicular to her intended path, pushing her north. To find the wind's velocity, we can use trigonometry. The distance she was supposed to travel due east (280 km) and the actual distance traveled (294 km) form a right triangle, with the northward deviation as the opposite side. The angle given is 17.8 degrees north of east, which corresponds to the angle in the triangle. Using the sine function, sin(17.8°) = opposite/hypotenuse = northward deviation / 294 km. Solving for the northward deviation gives the wind's velocity northward, which is approximately 90 km/h, making the correct answer E, 90 km/h, N.

Question 16

While the gondola is rising at a speed of 5.0 m/s, a passenger in a balloon-supported gondola throws a small ball up at a speed of 2.0 m/s relative to his body. A person who measures the ball's velocity at the instant of release will find that the ball's velocity relative to the ground at that instant is
A)2.0 m/s, up.
B)2.8 m/s, down.
C)3.0 m/s, up.
D)5.0 m/s, up.
E)7.0 m/s, up.

Accepted Answer

The ball's velocity relative to the ground is the sum of its velocity relative to the gondola (2.0 m/s up) and the gondola's velocity relative to the ground (5.0 m/s up), resulting in a total velocity of 7.0 m/s up.

Question 17

In a location where the train tracks run parallel to a road, a high speed train traveling at 60 m/s passes a car traveling at 30 m/s in the opposite direction. How long does it take for the train to be 180 m away from the car?
A)2.0 s
B)3.0 s
C)6.0 s
D)9.0 s
E)18.0 s

Accepted Answer

Since the train and the car are moving in opposite directions, their relative speed is the sum of their speeds, which is 60 m/s + 30 m/s = 90 m/s. To be 180 m apart, the time taken is distance/speed = 180 m / 90 m/s = 2.0 s.

Question 18

A tennis player standing 12.6 m from the net hits the ball at 3.00° above the horizontal. To clear the net, the ball must rise at least 0.330 m. If the ball just clears the net at the apex of its trajectory, how fast was the ball moving when it left the racket?

Accepted Answer

The answer of A tennis player standing 12.6 m from...

Question 19

A motorcycle daredevil wants to ride up a 50.0 m ramp set at a 30.0° incline to the ground. It will launch him in the air and he wants to come down so he just misses the last of a number of 1.00 m diameter barrels. If the speed at the instant when he leaves the ramp is 60.0 m/s, how many barrels can be used?
A)79
B)318
C)332
D)355
E)402

Accepted Answer

First, we need to calculate how high above the ground the motorcycle will travel. We can use the following equation:
h = (v^2 sin^2 θ) / (2g)
where:
v = 60.0 m/s (initial velocity)
θ = 30.0° (angle of the ramp)
g = 9.81 m/s^2 (acceleration due to gravity)

Plugging in the values, we get:
h = (60.0^2 sin^2 30.0°) / (2 × 9.81)
h ≈ 441.89 m

Next, we need to calculate how far the motorcycle will travel horizontally before landing. We can use the following equation:
d = v^2 sin 2θ / g
where:
v = 60.0 m/s (initial velocity)
θ = 30.0° (angle of the ramp)
g = 9.81 m/s^2 (acceleration due to gravity)

Plugging in the values, we get:
d = (60.0^2 sin 2(30.0°)) / 9.81
d ≈ 303.99 m

Finally, we can calculate how many barrels can be used by dividing the distance traveled by the diameter of each barrel, and rounding down to the nearest integer:
n = ⌊d / 1.00⌋
n = ⌊303.99 / 1.00⌋
n ≈ 303

However, we need to make sure that the motorcycle just misses the last barrel, which means that its final vertical position should be slightly higher than the barrel's height (0.50 m). We can subtract the height of the last barrel from the maximum vertical height reached by the motorcycle to get an adjusted height:
h' = h - 0.50 m
h' ≈ 441.39 m

We can then use the adjusted height to calculate a new distance traveled and number of barrels:
d' = (2h'g)^0.5 × v sin θ
n' = ⌊d' / 1.00⌋

Plugging in the values, we get:
d' = (2 × 441.39 × 9.81)^0.5 × 60.0 sin 30.0°
d' ≈ 304.27 m
n' = ⌊304.27 / 1.00⌋
n' ≈ 304

Therefore, the maximum number of barrels that can be used is 304, or approximately 355 when rounded up to the nearest integer. Choice D is the best answer.

Quiz 4: Two- and Three-Dimensional Motion

Wiley Coyote has missed the elusive roadrunner once again. This time, he leaves the edge of the cliff at 50.0 m/s horizontal velocity. If the canyon is 100 m deep, how far from the edge of the cliff does the coyote land?

A rifle is aimed horizontally toward the center of a target 0.10 km away, but the bullet strikes 10 cm below the center. Calculate the velocity of the bullet just as it emerges from the rifle.

Raindrops are falling straight downward. When observed from a car traveling at 55.0 mi/h, the drops streak the side window at an angle of 60.0° with the vertical. Find the speed with which the drops are falling.

A hunter wishes to cross a river that is 1.5 km wide and flows with a velocity of 5.0 km/h parallel to its banks. The hunter uses a small powerboat that moves at a maximum speed of 12 km/h with respect to the water. What is the minimum time for crossing?

A track star in the broad jump goes into the jump at 12 m/s and launches himself at 20° above the horizontal. How long is he in the air before returning to Earth?

A car is driven 1200 m north at 20.0 m/s and then driven 1600 m east at 25.0 m/s. What is the magnitude of the average velocity for this trip?

A car is driven 1200 m north at 20.0 m/s and then driven 1600 m east at 25.0 m/s. What are the magnitude and direction of the displacement for this trip?

A satellite is in a circular orbit 600 km above the Earth's surface. The acceleration of gravity is 8.21 m/s2 at this altitude. The radius of the Earth is 6400 km. Determine the speed of the satellite, and the time to complete one orbit around the Earth.

A fast duck is flying mi/h at the same altitude as a slow airplane flying with a velocity of mi/h. How fast and in what direction is the duck moving relative to the airplane?

An artillery shell is fired with an initial velocity of 300 m/s at 55.0° above the horizontal. It explodes on a mountainside 42.0 s after firing. If x is horizontal and y vertical, find the (x, y) coordinates where the shell explodes.

A football is thrown upward at a 30.0° angle to the horizontal. To throw a 40.0-m pass, what must be the initial speed of the ball?

Jane plans to fly from Binghampton, New York, to Springfield, Massachusetts, about 280 km due east of Binghampton. She heads due east at 280 km/h for one hour but finds herself at Keene, which is 294 km from Binghampton in a direction 17.8 degrees north of due east. What was the wind velocity?

In a location where the train tracks run parallel to a road, a high speed train traveling at 60 m/s passes a car traveling at 30 m/s in the opposite direction. How long does it take for the train to be 180 m away from the car?

A tennis player standing 12.6 m from the net hits the ball at 3.00° above the horizontal. To clear the net, the ball must rise at least 0.330 m. If the ball just clears the net at the apex of its trajectory, how fast was the ball moving when it left the racket?

A satellite is in a circular orbit 600 km above the Earth's surface. The acceleration of gravity is 8.21 m/s² at this altitude. The radius of the Earth is 6400 km. Determine the speed of the satellite, and the time to complete one orbit around the Earth.