A 25000kg bowling ball moving at 40 m/s hits a 10000kg bowling ball moving at 25 m/s from behind. It is a perfectly elastic collision, so what are the final velocities of the two balls?
To find the final velocities of the two balls after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Momentum (p) is defined as the product of mass (m) and velocity (v). So the momentum before the collision (initial momentum) can be calculated as:
Initial momentum = (mass1 * velocity1) + (mass2 * velocity2)
Given that the mass and velocity of the first ball are 25000 kg and 40 m/s, and the mass and velocity of the second ball are 10000 kg and 25 m/s, respectively, we can calculate the initial momentum:
Initial momentum = (25000 kg * 40 m/s) + (10000 kg * 25 m/s)
= 1000000 kg·m/s + 250000 kg·m/s
= 1250000 kg·m/s
Since the collision is perfectly elastic, the total momentum after the collision will also be 1250000 kg·m/s.
Now, let's assume the final velocities of the first and second balls are V1 and V2, respectively. The final momentum can be calculated as:
Final momentum = (mass1 * V1) + (mass2 * V2)
Given that the masses of the balls remain the same after the collision, the equation becomes:
Final momentum = (25000 kg * V1) + (10000 kg * V2)
Since the total momentum before the collision and after the collision are the same, we can set up the equation:
1250000 kg·m/s = (25000 kg * V1) + (10000 kg * V2)
Now, using this equation, we can solve for V1 and V2, which are the final velocities of the two balls.