Chapter 9.2, Problem 17PP

To determine

The final speed of the cars if they stick together after collision.

Answer to Problem 17PP

  $1.1\text{m/s}$

Explanation of Solution

Given:

The mass of each car, $m=3.0\times {10}^5\text{kg}$

The initial velocity of one car is, $v_{1i}=2.2\text{m/s}$

The other car was at rest; hence its initial velocity will be, $v_{2i}=0\text{m/s}$

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 two car 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 speed of the cars when they stick together after collision be $v_f$ , then using the law of conservation of linear momentum,

  $\begin{array}{c}{p}_i=p_f\\ m{v}_{1i}+m{v}_{2i}=\left(m+m\right)v_f\end{array}$

Using given values in above,

  $\begin{array}{c}\left(3\times {10}^5\right)\left(2.2\right)+\left(3\times {10}^5\right)\left(0\right)=2\left(3\times {10}^5\right)v_f\\ v_f=1.1\text{m/s}\end{array}$

Conclusion:

Thus, the final speed of the cars when they stick together after collision is $1.1\text{m/s}$ .