Respuesta :
To solve the question we must know about the conservation of momentum.
Conservation of Momentum
According to the law of conservation of momentum, when two bodies collide with each other then their momentum is conserved if no external force acts on the system. therefore, the combined momentum of the two objects before collision will be equal to the combined momentum of the two objects after the collision.
the momentum of the two objects before the collision
= momentum of the two objects after the collision
The mass of the box is 0.30141 kg.
Explanation
Given to us
- Mass of racquetball, m = 0.0427 kg,
- Velocity of racquetball before Collision, [tex]\bold{u_1}[/tex] = 22.3 m/s,
- Velocity of box before Collision,[tex]\bold{ u_2}[/tex] = 0 m/s,
- Velocity of racquetball after Collision, [tex]\bold{v_1}[/tex] = 11.5 m/s,
- Velocity of box after Collision, [tex]\bold{v_2}[/tex] = 1.53 m/s,
Assumption
Let the mass of the box be M.
Conservation Of Momentum
Momentum before collision = Momentum after collision
[tex]mu_1 + Mu_2 = mv_1 + Mv_2[/tex]
given, the box was stationary before the collision,
[tex]mu_1 + Mu_2 = mv_1 + Mv_2\\\\ mu_1 + 0 = mv_1 + Mv_2\\\\ mu_1 - mv_1 = Mv_2\\\\ M= \dfrac{mu_1 - mv_1}{v_2}[/tex]
Substituting the values,
[tex]M= \dfrac{mu_1 - mv_1}{v_2}\\\\ M = \dfrac{(0.0427 \times 22.3) - (0.0427\times 11.5)}{1.53}\\\\ M = 0.30141\ kg[/tex]
Hence, the mass of the box is 0.30141 kg.
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