Question

A 71.0 kg football player is gliding across very smooth ice at 2.15 m/s . He throws a 0.470 kg football straight forward. Part A What is the player's speed afterward if the ball is thrown at 18.0 m/s relative to the ground?

Answer 1

The player's speed afterward ball is thrown at 18
`(m)/(s)` relative to ground is 2.04
`(m)/(s)`

Step-by-step explanation:

Given:

Mass of football player
`m = 71` kg

Speed of player
`v = 2.15`
`(m)/(s)`

Mass of football
`m' = 0.470` kg

For finding the player's speed afterward the ball is thrown at 18
`(m)/(s)` relative to the ground,

The initial momentum of football player and ball is,

`P_(i) = (m+m') v`

`P_(i) = (71 +0.470) 2.15`

`P_(i) = 153.66`
`kg . (m)/(s)`

The final momentum of the system is,

`P_(f) = mv_(o) + m'v_(b)`

Here given in question
`v_(b) = 18 (m)/(s)`

`P_(f) = 71 v_(o) + 0.470 * 18`

Using the conservation of momentum,

`P_(i) = P_(f)`

`153.66 = 71 v_(o) + 0.470 * 18`

`71v_(o) = 145.2`

`v_(o) = 2.04`
`(m)/(s)`

Therefore, the player's speed afterward ball is thrown at 18
`(m)/(s)` relative to ground is 2.04
`(m)/(s)`