An 75 kg quarterback jumps straight up in the air right before throwing a 0.43 kg football horizontally at 11 m/s. How fast will he be moving backward just after releasing the ball?
To find the speed at which the quarterback will be moving backward just after releasing the ball, we can apply the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum before an event is equal to the total momentum after the event, provided that no external forces act on the system during the event.
In this case, we have two objects: the quarterback and the football. The momentum of an object is given by its mass multiplied by its velocity.
Before the quarterback throws the football, his total momentum is given by:
Momentum of the quarterback = mass of the quarterback * velocity of the quarterback
Momentum of the football = mass of the football * velocity of the football
Since the quarterback is jumping straight up in the air, his velocity can be considered as 0 m/s horizontally, and the velocity of the football is given as 11 m/s horizontally.
The momentum of the quarterback just before releasing the ball is therefore 0 kg*m/s (since his velocity is 0 m/s) and the momentum of the football just before being released is (0.43 kg) * (11 m/s) = 4.73 kg*m/s.
According to the principle of conservation of momentum, the total momentum after the event (the release of the ball) must also be equal to 4.73 kg*m/s.
After releasing the ball, the quarterback will be in motion due to the reaction force exerted on him by the ball. In this case, the quarterback will move in the opposite direction as the football was thrown. Let's assume the velocity of the quarterback after releasing the ball is v m/s.
To find the speed at which the quarterback is moving backward, we can set up the conservation of momentum equation:
Total momentum before = Total momentum after
(75 kg * 0 m/s) + (0.43 kg * 11 m/s) = (75 kg * v m/s)
0 + 4.73 kg*m/s = 75 kg * v m/s
Therefore, we can solve for v:
v = (4.73 kg*m/s) / (75 kg)
v ≈ 0.0631 m/s
So, the quarterback will be moving backward at approximately 0.0631 m/s just after releasing the ball.