A 1500-kg car traveling at 90 km/h toward the east suddenly collides with a 3000-kg car traveling at 60 km/h toward the south.The two cars stick together after the collision.What is the direction of motion of the cars after collision?

Question

Quizplus · Accepted Answer

We can use conservation of momentum in two dimensions to solve this problem. 
Before the collision, the 1500-kg car has a momentum of 1500 kg * 25 m/s = 37500 kg*m/s toward the east (since 90 km/h is 25 m/s) and the 3000-kg car has a momentum of 3000 kg * 16.67 m/s = 50010 kg*m/s toward the south (since 60 km/h is 16.67 m/s). 
After the collision, the two cars stick together and move with the same velocity. Let's call this velocity v. We can set up an equation for conservation of momentum in the x-direction: 
1500 kg * 25 m/s + 3000 kg * 0 m/s = (1500 kg + 3000 kg) * v_x 
where v_x is the x-component of the final velocity. Solving for v_x, we get v_x = 12.5 m/s. 
We can set up another equation for conservation of momentum in the y-direction: 
1500 kg * 0 m/s + 3000 kg * 16.67 m/s = (1500 kg + 3000 kg) * v_y 
where v_y is the y-component of the final velocity. Solving for v_y, we get v_y = 11.11 m/s. 
Finally, we can use trigonometry to find the direction of motion of the cars: 
tan(theta) = v_y / v_x 
theta = atan(v_y / v_x) 
theta = 53.1° south of east.

A 1500-Kg Car Traveling at 90 Km/h Toward the East