Question

A 40 tonnes rail car travels at 4km/h collides with a 100 tonnes wagon moving on the same track in the opposite direction at 1.2 km/h. Find their velocities immediately after impact assuming no loss of energy.

Answer 1

Weight of the rail car $(m_1)$ =40tons

Velocity $(u_1)$ =4Km/hour

Mass of the wagon$(m_2)$ =100 tons

Velocity of wagon$(u_2)$ =1.2k/hour

Let the final velocity of the rail wagon($v_1$) and the final velocity of wagon ($v_2$ )

Now, applying the conservation of the linear momentum.

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

$40v_1+100v_2=40 \times4-100\times1.2$

$\Rightarrow 40v_1+100v_2=160-120=40$

$\Rightarrow 2v_1+5v_2=2--------(i)$

The collision is elastic,

So, e=1

$e=\dfrac{v_2-v_1}{u_1-u_2}$

$\Rightarrow 1=\dfrac{v_2-v_1}{4-1.2}$

$v_2-v_1=2.8----(ii)$

From equation (i) and (ii)

$v_1=\dfrac{-12}{7} km/hour$

$v_2=\dfrac{7.6}{7}km/hour$