Chapter 9.2, Problem 18PP

To determine

The speed with which the goalie slide on the ice after catching the puck.

Answer to Problem 18PP

  $0.0335\text{m/s}$

Explanation of Solution

Given:

The mass of the hockey puck, $m_p=0.105\text{kg}$

The mass of the goalie, $m_g=75\text{kg}$

The initial velocity of the puck, $v_{pi}=24\text{}\text{m/s}$

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

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 the goalie 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 speed of the goalie after catching the puck be $v_f$ , then using the law of conservation of linear momentum,

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

Using given values in above,

  $\begin{array}{c}\left(75\right)\left(0\right)+\left(0.105\right)\left(24\right)=\left(75+0.105\right)v_f\\ v_f=0.0335\text{m/s}\end{array}$

Conclusion:

Thus, the speed of the goalie after catching the puck is $0.0335\text{m/s}$ .