Olaf is standing on a sheet of ice that covers the football stadium parking lot in Buffalo, New York; there is negligible friction between his feet and the ice. A friend throws Olaf a ball of mass 0.400 kg that is traveling horizontally at 10.4 m/s. Olaf's mass is 67.8 kg.
If the ball hits Olaf and bounces off his chest horizontally at 7.80 m/s in the opposite direction, what is his speed after the collision?
What was wrong with the previous response?
To find Olaf's speed after the collision, we can use 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.
Momentum is given by the product of an object's mass and velocity. Therefore, the momentum before the collision is equal to the momentum after the collision.
Before the collision:
Momentum of Olaf = mass of Olaf * velocity of Olaf
Momentum of ball = mass of ball * velocity of ball
After the collision:
Momentum of Olaf = mass of Olaf * velocity after collision (unknown)
According to the principle of conservation of momentum:
Momentum before the collision = Momentum after the collision
Therefore, we can write the equation as:
(mass of Olaf * velocity of Olaf) + (mass of ball * velocity of ball) = (mass of Olaf * velocity after collision)
Plugging in the given values:
(67.8 kg * velocity of Olaf) + (0.400 kg * 10.4 m/s) = (67.8 kg * velocity after collision)
Simplifying the equation:
67.8 kg * velocity of Olaf + 4.16 kg·m/s = 67.8 kg * velocity after collision
Since negligible friction is mentioned in the question, we can assume that there is no external force acting on the system after the collision. In such a case, momentum is conserved, and the total momentum before and after the collision will be the same.
Therefore, since the ball bounces off Olaf's chest horizontally, his velocity after the collision will be in the opposite direction. The magnitude of the velocity will remain the same.
So, the equation becomes:
67.8 kg * velocity of Olaf + 4.16 kg·m/s = -67.8 kg * velocity of Olaf
Now, we can solve for the velocity of Olaf after the collision.
67.8 kg * velocity of Olaf - 67.8 kg * velocity of Olaf = -4.16 kg·m/s
0 = -4.16 kg·m/s
Since the left-hand side of the equation is zero, we can conclude that the velocity of Olaf after the collision is zero.
Therefore, Olaf's speed after the collision is 0 m/s.