Question

A car of mass 1000 kg is heading east at 25 m/s. It collides with a car of mass 1200 kg heading north at 30 m/s. When the cars collide, they stick together.

d. At what angle do the cars move after the collision? (2 points)

Answer 1

Given :-

• A car of mass 1000 kg is heading east at 25 m/s.
• It collides with a car of mass 1200 kg heading north at 30 m/s.
• When the cars collide, they stick together.

To Find :-

• At what angle do the cars move after the collision?

Solution :-

Here it's given that a car of mass 1000kg moving with velocity of 25m/s North . Another car of mass 1200kg is moving with velocity 30m/s East.

So that ,

`v_(1)= 25m/s \ E= 25 \hat{i} m/s`

And ,

`v_(2)= 30m/s \ N = 30 \hat{j} m/s`

See attachment .

From Triangle law of vector addition , the resultant of both vectors will be given by third side of the triangle taken in opposite direction.

So , if the resultant velocity makes an angle
`\theta` . Then ,

`tan\theta = (v_2)/(v_1)`

Substituting the respective values,

`tan\theta =(30m/s)/(25m/s)`

Simplify ,

`tan\theta =(6)/(5)`

Take arctan both sides ,

`\theta = tan^(-1)\bigg((6)/(5)\bigg)`

Hence the cars move at an angle of tan-¹(6/5) NE after the collision .