A 45kg student is riding on a 7.0kg skateboard with a velocity of +4.0m/s. The student jumps off the board with a velocity of -1.0m/s. Find the velocity of the skateboard after the student jumped off.
This is a conservation of momentum problem. The total momentum of the system (student + skateboard) before the jump is equal to the total momentum after the jump.
Before the jump:
Total mass = 45 kg + 7 kg = 52 kg
Total momentum = (52 kg) x (4.0 m/s) = 208 kg*m/s
After the jump:
The mass of the skateboard remains the same, but the student is no longer on it. So the total mass is now just 7 kg. Let's call the velocity of the skateboard after the jump v:
Total mass = 7 kg
Total momentum = (7 kg) x v
According to conservation of momentum:
Total momentum before = Total momentum after
(52 kg) x (4.0 m/s) = (7 kg) x v
Solving for v, we get:
v = (52 kg x 4.0 m/s) / 7 kg
v = 29.71 m/s
So the velocity of the skateboard after the student jumped off is approximately 29.71 m/s. Note that this assumes no external forces (such as friction) act on the system.
This is a conservation of momentum problem. The total momentum of the system (student + skateboard) before the jump is equal to the total momentum after the jump.
Before the jump:
Total mass = 45 kg + 7 kg = 52 kg
Total momentum = (52 kg) x (4.0 m/s) = 208 kg*m/s
After the jump:
The mass of the skateboard remains the same, but the student is no longer on it. So the total mass is now just 7 kg. Let's call the velocity of the skateboard after the jump v:
Total mass = 7 kg
Total momentum = (7 kg) x v
According to conservation of momentum:
Total momentum before = Total momentum after
(52 kg) x (4.0 m/s) = (7 kg) x v
Solving for v, we get:
v = (52 kg x 4.0 m/s) / 7 kg
v = 29.71 m/s
So the velocity of the skateboard after the student jumped off is approximately 29.71 m/s. Note that this assumes no external forces (such as friction) act on the system.
A 5.0kg ball moving at 6.0m/s strikes a 3.0kg ball initially at rest. The 5.0kg ball continues moving in the same direction at 2.0m/s after the collision. Find the velocity of the 3.0kg ball.
A 5.0kg ball moving at 6.0m/s strikes a 3.0kg ball initially at rest. The 5.0kg ball continues moving in the same direction at 2.0m/s after the collision. Find the velocity of the 3.0kg ball.