Question

A 3 kg cart moves due east at 17m/s collides with a 5 kg cart moving due west. What is the initial speed of the 5 kg if the they stick together and come to rest.

Answer 1

The speed of 5 kg ball is 10.2 m/s

Given data:

The mass of cart 1 is m₁=3 kg.

The speed of cart 1 moving east is v₁=17 m/s.

The mass of other cart is m₂=5 kg.

Since the carts stick together, and comes to rest their final velocity is zero, i.e., v=0.

Applying the conservation of momentum between the carts as,

`m_1v_1+m_2v_2=(m_1+m_2)v`

Here, v₂ is the speed of 5kg cart. Since the cart 2 moving in west direction therefore v₂=-v₂.

Substitute all the values in above equation,

`\begin{gathered} 3(17)+5(-v_2)=(3+5)(0) \\ v_2=10.2\text{ m/s} \end{gathered}`

Thus, the speed of 5 kg ball is 10.2 m/s.

Final answer: 10.2 m/s