Question

A car of mass 1050 kg is moving towards east with a speed of 15 $m{s}^{-1}$. A truck is moving towards west. The mass of the truck is 6320 kg. both the vehicle collide head-on and remain locked together after the collision. Based on above information, answer the following question.

The speed of truck before the collision so that the vehicles comes to rest after collision is

• A. $6m{s}^{-1}$
• B. $2.5m{s}^{-1}$
• C. $7.5m{s}^{-1}$
• D. $5m{s}^{-1}$

Answer 1

The correct option is B

$2.5m{s}^{-1}$

Given

Mass $m_1$=1050 kg

Mass $m_2$=6320 kg

Velocity $v_1=15m{s}^{-1}$

velocity $v_2$=?

The vehicle come to rest finally, hence final velocity v=0

Concept of momentum

Since the final velocity is zero, the final momentum is zero.

$$\begin{gathered} -m_1{v}_1+m_2{v}_2=0 \\ {m}_1{v}_1=m_2{v}_2 \\ {v}_2=\frac{m_1}{m_2}{v}_1=\frac{1050}{6320}\times 15 \\ {v}_2=2.5m{s}^{-1} \end{gathered}$$

Therefore the vehicle comes to rest after the collision is $2.5m{s}^{-1}$

Hence option (b) is the right answer