Question

A 71.5 kg football player is gliding across very smooth ice at 2.00 m/s . He throws a 0.470 kg football straight forward. What is the player's speed afterward if the ball is thrown at 12.5 m/s relative to the ground? Express your answer with the appropriate units

Answer 1

Answer:

The player's speed is 1.93 m/s.

Explanation:

Given that,

Mass of football = 71.5 kg

Speed = 2.00 m/s

Mass of football = 0.470 Kg

Speed = 12.5 m/s

We need to calculate the initial momentum of the football player and ball

$P_{i}=(m+m_{b})v_{i}$

Put the value into the formula

$P_{i}=(71.5+0.470)\times2.00$

$P_{i}=143.94\ kg-m/s$

We need to calculate the final momentum of the system

$P_{f}=mv+m_{b}v_{b}$

Put the value into the formula

$P_{f}=71.5\times v+0.470\times12.5$

$P_{f}=71.5\times v+5.875$

We need to calculate the relative to the ground

Using conservation of momentum

$P_{i}=P_{f}$

Put the value into the formula

$143.94=71.5\times v+5.875$

$v=\dfrac{143.94-5.875}{71.5}$

$v=1.93\ m/s$

Hence, The player's speed is 1.93 m/s.