A 69.5kg football player is gliding across very smooth ice at 2.15m/s . He throws a 0.470kg football straight forward.
What is the player's speed afterward if the ball is thrown at 16.0m/s relative to the ground?
What is the player's speed afterward if the ball is thrown at 16.0m/s relative to the player?
initial momentum forward = (69.5+.47)(2.15)
= 150.4
so
150.4 = 69.5 v + .470*16
in second part
v ball = 2.15 + 16 = 18.15 m/s
150.4 = 69.5 v + .470*18.15
so you would get 2m/s for both however that is not correct
2.05
2.04
To answer this question, we can use the principle of conservation of momentum. According to this principle, the total momentum before the ball is thrown should be equal to the total momentum after the ball is thrown.
The momentum of an object can be calculated by multiplying its mass by its velocity. Therefore, the initial momentum of the system (player and football) before the ball is thrown can be calculated as follows:
Initial momentum of the system = (mass of the player × velocity of the player) + (mass of the football × velocity of the football)
Given that the mass of the player is 69.5 kg, the velocity of the player is 2.15 m/s, the mass of the football is 0.470 kg, and the velocity of the football with respect to the ground is 16.0 m/s, we can calculate the initial momentum of the system:
Initial momentum of the system = (69.5 kg × 2.15 m/s) + (0.470 kg × 16.0 m/s)
To calculate the final momentum of the system, we need to consider the momentum of the player alone and the momentum of the football alone.
Since the ball was thrown relative to the ground, the velocity of the player with respect to the ground remains the same (2.15 m/s). However, the velocity of the football with respect to the player must be calculated by subtracting the player's velocity (2.15 m/s) from the velocity of the football with respect to the ground (16.0 m/s). Therefore, the velocity of the football with respect to the player is 16.0 m/s - 2.15 m/s = 13.85 m/s.
Now, we can calculate the player's final momentum:
Final momentum of the player = mass of the player × velocity of the player
Final momentum of the player = 69.5 kg × 2.15 m/s
Finally, we can calculate the final momentum of the system by adding the final momentum of the player and the final momentum of the football:
Final momentum of the system = (Final momentum of the player) + (mass of the football × velocity of the football with respect to the player)
Final momentum of the system = (69.5 kg × 2.15 m/s) + (0.470 kg × 13.85 m/s)
Now, we can calculate the player's speed (or velocity) afterward by dividing the final momentum of the system by the player's mass:
Player's speed afterward = (Final momentum of the system) / (mass of the player)
Player's speed afterward = [(69.5 kg × 2.15 m/s) + (0.470 kg × 13.85 m/s)] / (69.5 kg)
To answer the second part of the question, where the ball is thrown relative to the player, we need to consider that the velocity of the ball with respect to the player is 16.0 m/s, since that is the given value.
We can proceed with the same calculations described above, but now we will use a velocity of 16.0 m/s for the football with respect to the player, instead of 13.85 m/s.
So, the only difference in the calculations will be in the value of the velocity of the football with respect to the player. Everything else will remain the same.
Player's speed afterward (when the ball is thrown relative to the player) = [(69.5 kg × 2.15 m/s) + (0.470 kg × 16.0 m/s)] / (69.5 kg)
By substituting the values in each equation, we can calculate the player's speed afterward in both scenarios.