Chapter 9, Problem 76A

To determine

The initial speed of the van if finally, the van and compact car move off together at $8.5\text{m/s}$ .

Answer to Problem 76A

  $11.22\text{m/s}$ in the direction of final velocity of van and car.

Explanation of Solution

Given:

The mass of the van, $m_v=2575\text{kg}$

The mass of the compact car, $m_c=825\text{kg}$

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

Final velocity of van and car, $v_f=8.5\text{m/s}$

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 car and van 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 initial speed of the van be $v_{vi}$ , then using the law of conservation of linear momentum,

  $\begin{array}{c}{p}_i=p_f\\ m_c{v}_{ci}+m_v{v}_{vi}=\left(m_c+m_v\right)v_f\end{array}$

Using given values in above,

  $\begin{array}{c}\left(825\right)\left(0\right)+\left(2575\right)\left(v_{vi}\right)=\left(2575+825\right)8.5\\ v_{2f}=11.22\text{m/s}\end{array}$

Conclusion:

Thus, the initial velocity of the van is $11.22\text{m/s}$ in the direction of final velocity of van and car.