Question

Problem B

A 1 kg cart A is initially at rest on a horizontal frictionless air track. A 0.2 kg cart B is
moving to the right at 10 meters per second on the same track. Cart B collides with
cart A causing cart A to move to the right at 3 meters per second.
17.- Calculate the velocity of cart B after the collision. Indicate the direction

Answer 1

`-5.0(m)/(s)` or
`5.0(m)/(s)` to the left

Step-by-step explanation:

The equation for an elastic collision is
`(m_1v_1)_i+(m_2v_2)_i=(m_1v_1)_f+(m_2v_2)_f`. Rearrange the equation for an elastic collision to solve for
`(v_2)_f`:

`([(m_1v_1)_i+(m_2v_2)_i-(m_1v_1)_f])/(m_2)`

For this problem, let

`m_1=1\ kg\\m_2=0.2\ kg\\(v_1)_i=0.0\ (m)/(s)\\(v_2)_i=10.0\ (m)/(s)\\(v_1)_f=3.0\ (m)/(s)`

So,

`([(1\ kg*0.0\ (m)/(s))+(0.2\ kg*10.0(m)/(s))-(1\ kg*3.0\ (m)/(s))])/(0.2\ kg)\\((0.0\ (kg*m)/(s))+(2.0\ (kg*m)/(s))-(3.0\ (kg*m)/(s)))/(0.2\ kg)\\(-1.0\ (kg*m)/(s))/(0.2\ kg)\\-5.0\ (m)/(s)`

This result indicates that cart B will move to the left after the collision.