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

The player's speed is 1.93 m/s.

Step-by-step 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)*2.00`

`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* v+0.470*12.5`

`P_(f)=71.5* 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* v+5.875`

`v=(143.94-5.875)/(71.5)`

`v=1.93\ m/s`

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