Question

Asked Mar 21, 2020

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**Collision at an Angle**

To apply conservation of linear momentum in an inelastic collision. Two cars, both of mass *m*, collide and stick together. Prior to the collision, one car had been traveling north at a speed 2*v*, while the second was traveling in a southeastern direction at an angle *ϕ* with respect to the east-west direction and at a speed *v*. After the collision, the two-car system travels in a northeastern direction at an angle *θ* with respect to the north-south direction and at a speed *v *final.

Find *v *final, the speed of the joined cars after the collision.

Express your answer in terms of *v* and *ϕ*.

Step 1

Given:

The mass of each car = m kg

The one car travelling north has speed = 2v m/s

The speed of another car = v m/s

The final speed = v_{f }m/s

Step 2

Solution:

To determine the final velocity, we will apply the momentum conservation along the North direction

Now applying the momentum conservation in east direction:

Step 3

On solving (1) and (2) we get:

We will be squaring and adding both equations to get the result:

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