A 69.5kg football player is gliding across very smooth ice at 2.15m/s . He throws a 0.470kg football straight forward.
A) What is the player's speed afterward if the ball is thrown at 16.0m/s relative to the ground?
B) What is the player's speed afterward if the ball is thrown at 16.0m/s relative to the player?
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To solve this problem, we can use the principle of conservation of momentum. The total momentum before the throw should be equal to the total momentum after the throw.
A) When the ball is thrown at 16.0 m/s relative to the ground:
Let's assume the speed of the football player after the throw is v1 and the speed of the ball after the throw is v2.
The initial momentum before the throw is given by:
initial momentum = (mass of the player × speed of the player) + (mass of the ball × speed of the ball)
= (69.5 kg × 2.15 m/s) + (0.470 kg × 0 m/s)
= 149.425 kg·m/s
The final momentum after the throw is given by:
final momentum = (mass of the player × speed of the player after the throw) + (mass of the ball × speed of the ball after the throw)
= (69.5 kg × v1) + (0.470 kg × 16 m/s) [since the speed of the ball is 16 m/s]
According to the conservation of momentum principle:
initial momentum = final momentum
149.425 kg·m/s = (69.5 kg × v1) + (0.470 kg × 16 m/s)
Solving for v1:
v1 = (149.425 kg·m/s - (0.470 kg × 16 m/s)) / 69.5 kg
v1 ≈ 2.12 m/s
Therefore, the player's speed afterward, when the ball is thrown at 16.0 m/s relative to the ground, is approximately 2.12 m/s.
B) When the ball is thrown at 16.0 m/s relative to the player:
In this case, the speed of the ball (16.0 m/s) is relative to the speed of the player, meaning the speed of the player does not change after the throw. Therefore, the player's speed afterward will still be 2.15 m/s.
In conclusion:
A) When the ball is thrown at 16.0 m/s relative to the ground, the player's speed afterward is approximately 2.12 m/s.
B) When the ball is thrown at 16.0 m/s relative to the player, the player's speed afterward is still 2.15 m/s.
To find the player's speed afterward in both scenarios, we can apply the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, provided no external forces are acting on the system. In this case, the system consists of the football player and the football.
The momentum of an object can be calculated by multiplying its mass by its velocity:
Momentum = mass × velocity
A) To find the player's speed afterward if the ball is thrown at 16.0 m/s relative to the ground:
1. Calculate the initial momentum before the throw (player + ball):
Initial momentum before = (player mass × player speed) + (ball mass × ball speed)
= (69.5 kg × 2.15 m/s) + (0.470 kg × 0 m/s) (since the ball is initially at rest)
= (69.5 kg × 2.15 m/s) + 0
= 149.425 kg·m/s
2. Calculate the final momentum after the throw:
Final momentum after = (player mass × player speed afterward) + (ball mass × ball speed afterward)
= (69.5 kg × player speed afterward) + (0.470 kg × 16 m/s)
3. Set the initial momentum equal to the final momentum and solve for the player's speed afterward:
Initial momentum before = Final momentum after
149.425 kg·m/s = (69.5 kg × player speed afterward) + (0.470 kg × 16 m/s)
Solving this equation will give you the player's speed afterward.
B) To find the player's speed afterward if the ball is thrown at 16.0 m/s relative to the player:
1. Calculate the initial momentum before the throw (player + ball):
Initial momentum before = (player mass × player speed) + (ball mass × ball speed relative to player)
= (69.5 kg × 2.15 m/s) + (0.470 kg × (-16 m/s)) (since the ball is thrown backward relative to the player)
2. Calculate the final momentum after the throw:
Final momentum after = (player mass × player speed afterward) + (ball mass × 0 m/s) (since the ball comes to rest relative to the player)
3. Set the initial momentum equal to the final momentum and solve for the player's speed afterward:
Initial momentum before = Final momentum after
Solving this equation will give you the player's speed afterward.
By following these steps and performing the necessary calculations, you can determine the player's speed afterward in both scenarios.