Problem 8.

A toy car “1” of mass 0.30 kg moves along a frictionless surface with a velocity of 0.20 m/s. It collides with another toy car “2”, with a mass of 0.40 kg and a speed of 0.10 m/s in the same direction. After the collision, toy car “1” continues to move in the same direction with a velocity of 0.15 m/s. Calculate the speed of toy car “2” after the collision.

Solution:

This problem is similar to problem 7.

We need to use the momentum conservation law: the net momentum of two toy cars before the collision is equal to the net momentum of two cars after the collision.

Then the net momentum of two cars is a vector sum of the momentum of car “1” and the momentum of car “2”.

Therefore, the initial net momentum of two cars is

A momentum of a car is a product of a mass of a car and its velocity. Then

The final momentum is

Then the momentum conservation law takes the form

or

............................(1)

To solve this vector equation we need to introduce coordinate system. Since we have motion along a line then it is enough to introduce only one axis: axis x (as shown in the figure).

We follow the standard procedure of finding the components of vectors and rewrite the vector equation (1) in terms of x-components:

x-component of equation (1):

Then