Question

A 0.0427 kg racquet-ball is moving

22.3 m/s when it strikes a
stationary box. The ball bounces
back at 11.5 m/s, while the box
moves forward at 1.53 m/s. What
is the mass of the box?
(Unit = kg)​

Answer 1

0.9433

Step-by-step explanation:

Answer 2

Mass of the box = 0.9433 kg

Step-by-step explanation:

Mass of racket-ball
`(m_1)` = 0.00427 kg

Velocity of racket-ball before collision
`(v_(1i))` = 22.3 m/s

Velocity of racket-ball after collision with box
`(v_(1f))` = -11.5 m/s

[Since ball is bouncing back, so velocity is taken negative.]

Velocity of the box before collision
`v_(2i)` = 0 m/s

[Since the box is stationary, so velocity is taken zero]

Velocity of box moving forward after collision
`v_(2f)`= 1.53 m/s

To find the mas of the box
`m_2`.

By law of conservation of momentum we have:

Momentum before collision = Momentum after collision

This can be written as:

`p_i=p_f`

`m_1v_(1i)+m_2v_(2i)=m_1v_(1f)+m_2v_(2f)`

We can plugin the given value to find
`m_2`

`(0.0427* 22.3)+(m_2* 0)=(0.0427* (-11.5))(m_2* 1.53)`

`0.9522+0=-0.4911+1.53m_2`

Adding both sides by 0.4911

`0.9522+0.4911=-0.4911+0.4911+1.53m_2`

`1.4433=1.53m_2`

Dividing both sides by 1.53.

`(1.4433)/(1.53)=(1.53m_2)/(1.53)`

`0.9433=m_2`

∴
`m_2=0.9433` kg

Mass of the box = 0.9433 kg (Answer)