Solved Examples

  1. Amy hits a 0.050-kg golf ball, giving it a speed of 75 m/s. What impulse does she impart to the ball?

    Solution: Because the impulse equals the change in momentum, you can reword this example to read, "What was the ball’s change in momentum?" It is also understood that the ball was initially at rest, so its initial speed was 0 m/s.

    Given: m = 0.050 kg Unknown: Δp = ?

    Δv = 75 m/s

    Original equation: Δp = m*Δv

    Solve: Δp = (0.050 kg)(75 m/s) = 3.75 kg m/s

  2. Wayne hits a stationary 0.12-kg hockey puck with a force that lasts for 0.010 s and makes the puck shoot across the ice with a speed of 20.0 m/s, scoring a goal for the team. With what force did Wayne hit the puck?
  3. Given: m = 0.12 kg; Unknown: F = ?

    Δv = 20.0 m/s

    Δt = 0.010 s


    Original equation: F*Δt = m*Δv


    Solve for the unknown: F = (m*Δv)/Δt

    = (0.12 kg)(20.0 m/s)/(0.010 s)

    = 240 N

  4. A tennis ball (of mass 0.060-kg) traveling at 10.0 m/s is returned by Andre Agassi. It leaves his racket with a speed of 36.0 m/s in the opposite direction from which it came.

  1. What is the change in momentum of the tennis ball?
  2. The change in velocity of the ball is 46.0 m/s since the ball reversed direction. Thus, the change in momentum is (mass) x (change in velocity) = (0.060 kg)(46.0 m/s) = 2.8 kg m/s.


  3. If the ball is in contact with the racket for 0.020 s, with what average force has Andre hit the ball?

    Use F = m*Δv/Δt => F = (0.060 kg)(46.0 m/s)/(0.020 s) => F = 140 N

Practice Exercises

  1. On April 15, 1912, the luxury cruiseliner Titanic sank after running into an iceberg.
  1. What momentum would the 450 000 000-kg ship have imparted to the iceberg if it had hit the iceberg head-on with a speed of 12.0 m/s? (Actually, the impact was a glancing blow.) (Remember . . . the Titanic stopped after the collision)
  2. If the captain of the ship had seen the iceberg a kilometer ahead and had tried to slow down, why would this have been a futile effort?
2.  Auto companies frequently test the safety of automobiles by putting them through crash tests to observe the integrity of the passenger compartment. If a 1000-kg car is sent toward a cement wall with a speed of 15 m/s and the impact brings it to a stop in 0.03 seconds, with what average force is it brought to rest?

3.  If 300 million (300 000 000) people in the United States jumped up in the air simultaneously, pushing off the earth with an average force of 1000 N each for a time of 0.10 s, what would happen to the earth (mass = 6 000 000 000 000 000 000 000 000 kg)?

4.  Bernie, whose mass is 70.0 kg, leaves a ski jump with a velocity of 21.0 m/s. What is Bernie’s momentum as he leaves the ski jump?

5.  Ethel is sitting on a park bench feeding the pigeons when a child’s ball rolls toward her across the grass. Ethel returns the ball to the child by hitting it with her 2.0-kg purse with a speed of 20 m/s. If the impact lasts for 0.4 s, with what force does Ethel hit the ball?

6.  When Sammy Sosa stepped up to the plate and hit a 0.150-kg fast ball traveling at 35.0 m/s, the impact caused the ball to leave his bat with a velocity of 45.0 m/s in the opposite direction. If the impact lasted for 0.002 s, what force did Sosa exert on the baseball?



1. (a) 5 400 000 000 kg m/s

   (b)  The ship was so big that even if the iceberg had been spotted a kilometer away, the ship could not have been turned in time to avoid the iceberg.

2.  -500 000 N

3.  0.000 000 000 000 5 m/s – this change in velocity is too small to be noticed!

4.  1470 kg m/s

5.  100 N

6.  6000 N