Question

A railway car having a total mass of 5.8 × 105 kg, moving with a speed of 9.1 km/h, strikes another car that has a mass of 8.7 × 105 kg and is initially at rest. The speed of the coupled cars after the collision is

A) 9.1 km/h.
B) 7.2 km/h.
C) 3.6 km/h.
D) 1.8 km/h.
E) 4.2 km/h

Answer 1

Answer:

Final speed of both the cars, V = 3.28 km/h

Explanation:

It is given that,

Mass of the railway car, $m_1=5.8\times 10^5\ kg$

Initial speed of the railway car, $u_1=9.1\ km/h=2.52\ m/s$

Mass of another car, $m_2=8.7\times 10^5\ kg$

Initial speed of another car, $u_2=0$

To find,

The speed of the coupled cars after the collision.

Solution,

It is a case of inelastic collision in which the linear momentum before and after the collision remains same. Let V is the coupled velocity of both of the cars. So,

$m_1u_1+m_2u_2=(m_1+m_2)V$

$V=\dfrac{m_1u_1+m_2u_2}{(m_1+m_2)}$

$V=\dfrac{m_1u_1}{(m_1+m_2)}$

$V=\dfrac{5.8\times 10^5\times 2.52778}{(5.8\times 10^5+8.7\times 10^5)}$

V = 1.011 m/s

or

V = 3.28 km/h

So, the speed of the coupled cars after the collision is 3.28 km/h. Hence, this is the required solution.