A rock (m = 1.5 kg) moving at 4.2 m/s north collides with a ball (m = 0.061 kg) that is initially at rest. What is the velocity of the rock after the collision if the velocity of the ball after the collision was 8.4 m/s north?
Initial north momentum = 1.5*4.2 = 6.3
which is also the final momentum
6.3 = .061 * 8.4 + 1.5 * v
v = 3.86 m/s
All motion remains in the north direction. Apply conservation of linear momentum in that direction.
Mrock*Vrock,initial = Mball*Vball + Mrock*Vrock,final
1.5*4.2 = 0.061*8.4 + 1.5*Vrock,final
Vrock,final = 3.86 m/s
The rock's direction remains north (positive)
To find the velocity of the rock after the collision, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass by its velocity.
Initially, the rock is moving at 4.2 m/s north, so its momentum is given by:
Momentum of the rock before the collision = mass of the rock * velocity of the rock before the collision
= 1.5 kg * 4.2 m/s north
The ball is initially at rest, so its momentum is zero:
Momentum of the ball before the collision = mass of the ball * velocity of the ball before the collision
= 0.061 kg * 0 m/s
The total momentum before the collision is then the sum of the momenta of the rock and the ball:
Total momentum before the collision = Momentum of the rock before the collision + Momentum of the ball before the collision
After the collision, the ball moves at 8.4 m/s north, so its momentum is given by:
Momentum of the ball after the collision = mass of the ball * velocity of the ball after the collision
= 0.061 kg * 8.4 m/s north
To find the velocity of the rock after the collision, we subtract the momentum of the ball after the collision from the total momentum before the collision and divide by the mass of the rock:
Velocity of the rock after the collision = (Total momentum before the collision - Momentum of the ball after the collision) / mass of the rock
Substituting the given values:
Velocity of the rock after the collision = (1.5 kg * 4.2 m/s north - 0.061 kg * 8.4 m/s north) / 1.5 kg
Now we can calculate the result.