Joe is sledding down a snow hill when he collides with Mike half way down the hill. Joe and the sled have a mass of 65 kg and their velocity before the collision was 12 m/s. If Mike has a mass of 55 kg, what velocity would Joe, Mike, and the sled have after the collision?
To determine the velocity of Joe, Mike, and the sled after the collision, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass by its velocity. So, we can determine the initial momentum before the collision as follows:
Initial momentum = (mass of Joe and sled) × (velocity before the collision)
+ (mass of Mike) × (velocity before the collision)
Initial momentum = (65 kg) × (12 m/s) + (55 kg) × (12 m/s)
To find the total momentum after the collision, we'll assume that momentum is conserved and that Joe and Mike move together after the collision. Therefore, they will have one common velocity, let's call it v. So, the total momentum after the collision can be written as:
Total momentum after the collision = (mass of Joe and sled + mass of Mike) × (velocity after the collision)
Since momentum is conserved, we can equate the expressions for initial and final momentum:
(65 kg) × (12 m/s) + (55 kg) × (12 m/s) = (65 kg + 55 kg) × v
Simplifying the equation, we can solve for v:
(65 kg + 55 kg) × v = (65 kg) × (12 m/s) + (55 kg) × (12 m/s)
120 kg × v = (65 kg) × (12 m/s) + (55 kg) × (12 m/s)
v = [(65 kg) × (12 m/s) + (55 kg) × (12 m/s)] / 120 kg
v = (780 kg·m/s + 660 kg·m/s) / 120 kg
v = 1440 kg·m/s / 120 kg
v = 12 m/s
Therefore, Joe, Mike, and the sled would have a velocity of 12 m/s after the collision.