Chapter 9, Problem 73A

To determine

The velocity and the direction in which K jumps.

Answer to Problem 73A

  $1.26\text{m/s}$ in the same direction as that of initial motion

Explanation of Solution

Given:

The mass of K, $m_K=42.00\text{kg}$

The mass of skateboard, $m_S=2.00\text{kg}$

The initial speed of K and skateboard, $v_i=1.20\text{m/s}$

After K jumps, the skateboard stops. Hence, the final velocity of skateboard, $v_f=0\text{m/s}$

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 K and the skateboard 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 motion of Kas positive.

Let, the final speed of K be $v_{Kf}$ , then using the law of conservation of linear momentum,

  $\begin{array}{c}{p}_i=p_f\\ \left(m_K+m_S\right)v_i=m_K{v}_{Kf}+m_S{v}_{Sf}\end{array}$

Using given values in above,

  $\begin{array}{c}\left(42+2\right)\left(1.2\right)=\left(42\right)\left(v_{Kf}\right)+\left(2\right)\left(0\right)\\ v_{Kf}=1.26\text{m/s}\end{array}$

Positive sign of the above velocity denotes that K jumps in the initial direction of motion.

Conclusion:

Thus, the velocity with which Kjumps is $1.26\text{m/s}$ in the same direction as that of initial motion.