Question 1

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 2

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 3

A 0.20-km wide river has a uniform flow speed of 3.0 m/s toward the east.A boat with a speed of 8.0 m/s relative to the water leaves the south bank and heads in such a way that it crosses to a point directly north of its departure point.How long does it take the boat to cross the river?
A)29 s
B)23 s
C)25 s
D)27 s
E)17 s

Accepted Answer

The answer of A 0.20-km wide river has a uniform...

Question 4

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 5

A football is thrown upward at a 30.0$\degree$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 6

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.How long does it take for the train to be 180 m ahead of the car?
A)2.0 s
B)3.0 s
C)6.0 s
D)9.0 s
E)18.0 s

Accepted Answer

The relative velocity between the train and the car is 60 m/s - 30 m/s = 30 m/s. 
To cover a distance of 180 m at this relative velocity, the time required is:
time = distance/relative velocity = 180 m/30 m/s = 6.0 s. 
Therefore, the train will be 180 m ahead of the car in 6.0 s.

Question 7

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 8

An artillery shell is fired with an initial velocity of 300 m/s at 55.0$\degree$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 9

The pilot of an aircraft flies due north relative to the ground in a wind blowing 40 km/h toward the east.If his speed relative to the ground is 80 km/h,what is the speed of his airplane relative to the air?
A)89 km/h
B)85 km/h
C)81 km/h
D)76 km/h
E)72 km/h

Accepted Answer

The speed of the airplane relative to the air can be found using the Pythagorean theorem, considering the northward speed (80 km/h) and the eastward wind speed (40 km/h) as perpendicular components of the airplane's velocity relative to the air. Thus, the airplane's speed relative to the air is $\sqrt{80^2 + 40^2} = \sqrt{6400 + 1600} = \sqrt{8000} = 89.44$ km/h, which rounds to 89 km/h.

Question 10

A car travels in a due northerly direction at a speed of 55 km/h.The traces of rain on the side windows of the car make an angle of 60 degrees with respect to the horizontal.If the rain is falling vertically with respect to the earth,what is the speed of the rain with respect to the earth?
A)48 km/h
B)95 km/h
C)58 km/h
D)32 km/h
E)80 km/h

Accepted Answer

The answer of A car travels in a due northerly...

Question 11

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 12

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 6 400 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 13

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$\degree$ with the vertical.Find the speed with which the drops are falling.

Accepted Answer

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

Question 14

A river has a steady speed of 0.30 m/s.A student swims downstream a distance of 1.2 km and returns to the starting point.If the student swims with respect to the water at a constant speed and the downstream portion of the swim requires 20 minutes,how much time is required for the entire swim?
A)50 minutes
B)80 minutes
C)90 minutes
D)70 minutes
E)60 minutes

Accepted Answer

The answer of A river has a steady speed of...

Question 15

A boat moves at 10.0 m/s relative to the water.If the boat is in a river where the current is 2.0 m/s,how long does it take the boat to make a complete round trip of 1.00 km upstream followed by a 1.00 km trip downstream?

Accepted Answer

The answer of A boat moves at 10.0 m/s relative...

Question 16

A tennis player standing 12.6 m from the net hits the ball at 3.00$\degree$ 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 17

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 18

A track star in the broad jump goes into the jump at 12 m/s and launches himself at 20$\degree$ 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 19

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 20

A student in the front of a school bus tosses a ball to another student in the back of the bus while the bus is moving forward at constant velocity.The speed of the ball as seen by a stationary observer in the street:
A)is less than that observed inside the bus.
B)is the same as that observed inside the bus.
C)is greater than that observed inside the bus.
D)may be either greater or smaller than that observed inside the bus.
E)may be either greater,smaller,or equal to that observed inside the bus.

Accepted Answer

The answer of A student in the front of a...

Quiz 3: Motion in Two Dimensions

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.

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 0.20-km wide river has a uniform flow speed of 3.0 m/s toward the east.A boat with a speed of 8.0 m/s relative to the water leaves the south bank and heads in such a way that it crosses to a point directly north of its departure point.How long does it take the boat to cross the river?

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

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.How long does it take for the train to be 180 m ahead of the car?

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?

An artillery shell is fired with an initial velocity of 300 m/s at 55.0 $\degree$ 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.

The pilot of an aircraft flies due north relative to the ground in a wind blowing 40 km/h toward the east.If his speed relative to the ground is 80 km/h,what is the speed of his airplane relative to the air?

A car travels in a due northerly direction at a speed of 55 km/h.The traces of rain on the side windows of the car make an angle of 60 degrees with respect to the horizontal.If the rain is falling vertically with respect to the earth,what is the speed of the rain with respect to the earth?

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 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 6 400 km.Determine the speed of the satellite,and the time to complete one orbit around the Earth.

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 $\degree$ with the vertical.Find the speed with which the drops are falling.

A river has a steady speed of 0.30 m/s.A student swims downstream a distance of 1.2 km and returns to the starting point.If the student swims with respect to the water at a constant speed and the downstream portion of the swim requires 20 minutes,how much time is required for the entire swim?

A boat moves at 10.0 m/s relative to the water.If the boat is in a river where the current is 2.0 m/s,how long does it take the boat to make a complete round trip of 1.00 km upstream followed by a 1.00 km trip downstream?

A tennis player standing 12.6 m from the net hits the ball at 3.00 $\degree$ 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?

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

A student in the front of a school bus tosses a ball to another student in the back of the bus while the bus is moving forward at constant velocity.The speed of the ball as seen by a stationary observer in the street:

Quiz 3: Motion in Two Dimensions

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.

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 0.20-km wide river has a uniform flow speed of 3.0 m/s toward the east.A boat with a speed of 8.0 m/s relative to the water leaves the south bank and heads in such a way that it crosses to a point directly north of its departure point.How long does it take the boat to cross the river?

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

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.How long does it take for the train to be 180 m ahead of the car?

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?

An artillery shell is fired with an initial velocity of 300 m/s at 55.0 °\degree° 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.

The pilot of an aircraft flies due north relative to the ground in a wind blowing 40 km/h toward the east.If his speed relative to the ground is 80 km/h,what is the speed of his airplane relative to the air?

A car travels in a due northerly direction at a speed of 55 km/h.The traces of rain on the side windows of the car make an angle of 60 degrees with respect to the horizontal.If the rain is falling vertically with respect to the earth,what is the speed of the rain with respect to the earth?

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 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 6 400 km.Determine the speed of the satellite,and the time to complete one orbit around the Earth.

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 °\degree° with the vertical.Find the speed with which the drops are falling.

A river has a steady speed of 0.30 m/s.A student swims downstream a distance of 1.2 km and returns to the starting point.If the student swims with respect to the water at a constant speed and the downstream portion of the swim requires 20 minutes,how much time is required for the entire swim?

A boat moves at 10.0 m/s relative to the water.If the boat is in a river where the current is 2.0 m/s,how long does it take the boat to make a complete round trip of 1.00 km upstream followed by a 1.00 km trip downstream?

A tennis player standing 12.6 m from the net hits the ball at 3.00 °\degree° 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?

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

A student in the front of a school bus tosses a ball to another student in the back of the bus while the bus is moving forward at constant velocity.The speed of the ball as seen by a stationary observer in the street:

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

An artillery shell is fired with an initial velocity of 300 m/s at 55.0 $\degree$ 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 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 6 400 km.Determine the speed of the satellite,and the time to complete one orbit around the Earth.

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 $\degree$ with the vertical.Find the speed with which the drops are falling.

A tennis player standing 12.6 m from the net hits the ball at 3.00 $\degree$ 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 track star in the broad jump goes into the jump at 12 m/s and launches himself at 20 $\degree$ above the horizontal.How long is he in the air before returning to Earth?