A body of mass 4kg moving with a velocity of 10 meter per second collide with a stationary body of mass 6kg. If the two body move together after the collision, calculate their common velocity

Answer 1

To solve this problem, we can use the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.

Let's denote the initial velocity of the stationary body as v2 (since it is stationary, its initial velocity is 0). Let's also denote the final common velocity of both bodies after the collision as v_f.

The total momentum before the collision is given by:
Initial momentum = (mass1 * velocity1) + (mass2 * velocity2)
= (4 kg * 10 m/s) + (6 kg * 0 m/s)
= 40 kg m/s + 0 kg m/s
= 40 kg m/s

The total momentum after the collision is given by:
Final momentum = (mass1 + mass2) * velocity_f

According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore, we can write:

40 kg m/s = (4 kg + 6 kg) * velocity_f

Now we can solve for the final common velocity (velocity_f):

40 kg m/s = 10 kg * velocity_f

Dividing both sides of the equation by 10 kg gives:

velocity_f = 40 kg m/s / 10 kg
= 4 m/s

Therefore, the common velocity of the two bodies after the collision is 4 m/s.