a 78kg hockey player standing on frictionless ice throws a 6.0kg bowling ball horizontally with a speed of 3.0m/s. With what speed does the hockey player recoil?
m1=78 kg, m2 =6 kg, v2 = 3m/s, v1 =?
0 = m1•v1 – m2•v2,
v1 = m2•v2/m1
To determine the speed at which the hockey player recoils, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision. In this case, the momentum of the system comprised of the hockey player and the bowling ball is conserved.
The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v): p = m * v.
Before the collision, the hockey player has a mass of 78 kg and is initially at rest, meaning their velocity (v) is 0 m/s. The bowling ball has a mass of 6.0 kg and is thrown horizontally with a speed (v) of 3.0 m/s.
The initial total momentum of the system can be calculated as:
Initial momentum = (mass of hockey player) * (initial velocity of hockey player) + (mass of bowling ball) * (initial velocity of bowling ball)
Initial momentum = (78 kg) * (0 m/s) + (6.0 kg) * (3.0 m/s)
Since the hockey player is initially at rest, their initial velocity is 0. Thus, the initial momentum simplifies to:
Initial momentum = (6.0 kg) * (3.0 m/s)
Now, we need to determine the final velocity of the hockey player after the collision. Since the bowling ball is thrown horizontally, there is no vertical force acting on the system. Therefore, the net horizontal momentum before and after the collision is conserved.
Final momentum = (mass of hockey player) * (final velocity of hockey player) + (mass of bowling ball) * (final velocity of bowling ball)
Since the hockey player is recoiling, we assume their final velocity is in the opposite direction to that of the bowling ball. The final velocity of the bowling ball can be determined using the conservation of momentum equation:
(6.0 kg) * (3.0 m/s) = (78 kg + 6.0 kg) * (final velocity of hockey player)
Simplifying the equation:
(6.0 kg) * (3.0 m/s) = (84 kg) * (final velocity of hockey player)
Now we can solve for the final velocity of the hockey player:
(final velocity of hockey player) = (6.0 kg * 3.0 m/s) / (84 kg)
(final velocity of hockey player) = 0.214 m/s
Therefore, the hockey player recoils with a speed of approximately 0.214 m/s in the opposite direction of the thrown bowling ball.