Chapter 9, Problem 8STP

To determine

To Choose: The correct option.

Answer to Problem 8STP

  A. $0.059\text{m/s}$

Explanation of Solution

Given:

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

The mass of the goalie, $m_g=82\text{kg}$

The initial velocity of the puck, $v_{pi}=46\text{}\text{m/s}$

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.

Assume the initial direction of hockey puck’s motion be positive.

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,

  $\begin{array}{c}\left(82\right)\left(0\right)+\left(0.105\right)\left(46\right)=\left(82+0.105\right)v_f\\ v_f\approx 0.059\text{m/s}\end{array}$

Conclusion:

Thus, the speed of the goalie with which the goalie slide after catching the puck is $0.059\text{m/s}$ .