Question

In an experiment, the 1 kg cart collides with a 3 kg cart but doesn’t stick to it. Instead, the 3 kg cart gets knock forward by the 1 kg cart at 0.30m/s, which comes to rest after the collision.
If the positive direction is to the right, what was the initial velocity of the 1.0-kg cart?

Answer 1

Explanation:

Given that,

Mass of the cart, $m_1=1\ kg$

Mass of the cart 2, $m_2=3\ kg$            

Final speed of cart 2, $v_2=0.3\ m/s$

Final speed of cart 1 is 0 as it comes to rest.

Let us assume that the initial velocity of the cart 2 is 0. So using the conservation of linear momentum as :

$m_1u_1+m_2u_2=m_1v_1+m_2v_2\\\\m_1u_1+0=0+m_2v_2\\\\m_1u_1=m_2v_2\\\\u_1=\dfrac{m_2v_2}{m_1}\\\\u_1=\dfrac{3\times 0.3}{1}\\\\u_1=0.9\ m/s$

So, the initial velocity of the 1.0-kg cart is 0.9 m/s.