Chapter 9, Problem 91A

To determine

The velocity of the puck and the jacket if they slide off together.

Answer to Problem 91A

  $8.38\text{m/s}$

Explanation of Solution

Given:

The mass of the hockey puck, $m_p=0.115\text{kg}$

The mass of the jacket, $m_j=0.365\text{kg}$

Initial velocity of the puck, $v_{pi}=35.0\text{}\text{m/s}$

Since the jacket was at rest initially, thus the initial velocity of the jacket, $v_{ji}=0\text{m/s}$

Formula used:

Momentum of an object of mass m and moving with velocity v is given by,

  $p=mv$

And, law of conservation of linear momentum: Momentum is conserved in a closed and isolated system and is given by,

  $p_i=p_f$

Calculation:

Consider the puck and jacket as a system, then it will be a closed and isolated system and law of conservation of momentum can be applied to it.

Let, the final velocity of the puck and jacket be $v_f$ , then using the law of conservation of linear momentum,

  $\begin{array}{c}{p}_i=p_f\\ m_p{v}_{pi}+m_j{v}_{ji}=\left(m_p+m_j\right)v_f\end{array}$

Using given values in above,

  $\begin{array}{c}{m}_p{v}_{pi}+m_j{v}_{ji}=\left(m_p+m_j\right)v_f\\ \left(0.115\right)\left(35\right)+\left(0.365\right)\left(0\right)=\left(0.115+0.365\right)v_f\\ v_f=8.38\text{m/s}\end{array}$

Conclusion:

Thus, the velocity of the puck and the jacket when they slide off together is $8.38\text{m/s}$ .