A 60 kg body moving with a speed of 5.0 m/s collides with a body twice its weight and moving at half its speed along the same direction. After the collision, the 60 kg body moves in the opposite direction with a speed of 2 m/s. Find the final velocity of the heavier body

To solve this problem, we need to use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.

Step 1: Calculate the initial momentum of both bodies before the collision.

The momentum (p) of an object is given by the product of its mass (m) and velocity (v), p = mv.

For the 60 kg body: p1_initial = m1 * v1 = 60 kg * 5.0 m/s = 300 kgm/s For the 120 kg body: p2_initial = m2 * v2 = 120 kg * 2.5 m/s = 300 kgm/s

The total initial momentum (p_initial) is the sum of the individual momenta: p_initial = p1_initial + p2_initial = 300 kgm/s + 300 kgm/s = 600 kg*m/s

Step 2: Calculate the final momentum of the 60 kg body after the collision.

The 60 kg body is moving in the opposite direction after the collision, so its velocity is -2 m/s (the negative sign indicates the opposite direction).

For the 60 kg body: p1_final = m1 * v1' = 60 kg * -2 m/s = -120 kg*m/s

Step 3: Calculate the final momentum of the 120 kg body after the collision.

We don't know the final velocity (v2') of the 120 kg body yet, that's what we're trying to find. But we can express its final momentum (p2_final) in terms of v2': p2_final = m2 * v2' = 120 kg * v2'

Step 4: Use the conservation of momentum to find v2'.

The total final momentum (p_final) is the sum of the individual final momenta: p_final = p1_final + p2_final = -120 kg*m/s + 120 kg * v2'

But from the conservation of momentum, we know that p_final = p_initial. So we can set up the following equation and solve for v2':

-120 kgm/s + 120 kg * v2' = 600 kgm/s 120 kg * v2' = 600 kgm/s + 120 kgm/s 120 kg * v2' = 720 kgm/s v2' = 720 kgm/s / 120 kg = 6 m/s

So the final velocity of the heavier body is 6 m/s.