A 35.0 kg kid run with a horizontal velocity of 5.50 m/s and jumps
onto a 5.00 kg sled. What is the velocity of the kid and sled after the
impact, if there were no friction? (4.81 m/s)
To calculate the velocity of the kid and sled after the impact, we can use the law of conservation of momentum. According to this law, the total momentum before the impact is equal to the total momentum after the impact, provided there are no external forces acting on the system.
The momentum of an object can be calculated by multiplying its mass by its velocity. Let's denote the velocity of the kid before the impact as v1, the velocity of the sled before the impact as v2, and the velocity of both the kid and sled after the impact as vf.
Before the impact, the kid and sled are separate objects, so the initial momentum is the sum of their individual momenta:
Initial momentum (before impact) = (mass of kid * velocity of kid) + (mass of sled * velocity of sled)
= (35.0 kg * 5.50 m/s) + (5.00 kg * 0 m/s) (since the sled is initially at rest)
= 192.5 kg·m/s
After the impact, the kid and sled move together as one object, so the final momentum is the product of their combined mass and velocity:
Final momentum (after impact) = (mass of kid + mass of sled) * velocity of kid + sled
= (35.0 kg + 5.00 kg) * vf (since they move as one object)
= 40.0 kg * vf
According to the law of conservation of momentum, the initial momentum is equal to the final momentum:
Initial momentum = Final momentum
192.5 kg·m/s = 40.0 kg * vf
Now, we can solve for the velocity of the kid and sled after the impact (vf):
vf = 192.5 kg·m/s / 40.0 kg
vf = 4.81 m/s
Therefore, the velocity of the kid and sled after the impact, if there were no friction, is 4.81 m/s.