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A 70.0 kg football player is gliding across very smooth
Chapter 9, Problem 22E(choose chapter or problem)
Problem 22E
A 70.0 kg football player is gliding across very smooth ice at 2.00 m/s. He throws a 0.450 kg football straight forward. What is the player’s speed afterward if the ball is thrown at
a. 15.0 m/s relative to the ground?
b. 15.0 m/s relative to the player?
Questions & Answers
QUESTION:
Problem 22E
A 70.0 kg football player is gliding across very smooth ice at 2.00 m/s. He throws a 0.450 kg football straight forward. What is the player’s speed afterward if the ball is thrown at
a. 15.0 m/s relative to the ground?
b. 15.0 m/s relative to the player?
ANSWER:
Step 1 of 2
a) We need to find out the player's speed if the ball's velocity is \(15 \mathrm{~m} / \mathrm{s}\) relative to the ground.
Using the conservation of momentum we can write,
\(m_{P}\left(v_{f}\right)_{P}+m_{B}\left(v_{f}\right)_{B}=m_{B} v_{i}+m_{P} v_{i}\)
\(m_{P}\left(v_{f}\right)_{P}+m_{B}\left(v_{f}\right)_{B}=\left(m_{B}+m_{P}\right) v_{i}\)
That is,
\(m_{P}\left(v_{f}\right)_{P}=\left(m_{B}+m_{P}\right) v_{i}-m_{B}\left(v_{f}\right)_{B}\)
Implies,
\(\left(v_{f}\right)_{P}=\frac{\left(m_{B}+m_{P}\right) v_{i}-m_{B}\left(v_{f}\right)_{B}}{m_{P}}\)
Mass of the ball is, \(m_{B}=0.450 \mathrm{~kg}\)
Mass of the person, \(m_{P}=70 \mathrm{~kg}\)
Final velocity of the ball, \(\left(v_{f}\right)_{B}=15 \mathrm{~m} / \mathrm{s}\)
Initial velocity of the person is equal to the initial velocity of the ball, \(v_{i}=2 \mathrm{~m} / \mathrm{s}\)
So the final velocity of the person,
\(\left(v_{f}\right)_{P} =\frac{(0.450 \mathrm{~kg}+70 \mathrm{~kg})(2 \mathrm{~m} / \mathrm{s})-(0.450 \mathrm{~kg})(15 \mathrm{~m} / \mathrm{s})}{70 \mathrm{~kg}}\)
\(\left(v_{f}\right)_{P} =1.92 \mathrm{~m} / \mathrm{s}\)
The final velocity of the person is \(1.92 \mathrm{~m} / \mathrm{s}\)