f a 57.0 g tennis ball is traveling horizontally at 72.0 m/s (which does occur), and a 55.0 { kg} tennis player leaps vertically upward and hits the ball, causing it to travel at 48.0 m/s in the reverse direction, how fast will her center of mass be moving horizontally just after hitting the ball?
Use the law of conservation of linear momentum. The change in the ball's momentum, which is 0.057 kg*(72+48 m/s), is equal and opposite to the change in player's momentum.
still i can't get the answer
To find the horizontal speed of the tennis player's center of mass just after hitting the ball, we need to apply the principle of conservation of momentum.
The initial momentum of the tennis ball before the collision is given by:
Momentum_ball_initial = Mass_ball × Speed_ball_initial
The final momentum of the tennis ball after the collision is given by:
Momentum_ball_final = Mass_ball × Speed_ball_final
According to the conservation of momentum principle, the initial momentum of the tennis ball must be equal to the final momentum. Therefore:
Momentum_ball_initial = Momentum_ball_final
Let's solve this step-by-step:
1. Convert the mass of the tennis ball from grams to kilograms:
Mass_ball = 57.0 g ÷ 1000 = 0.057 kg
2. Use the momentum equation to find the initial momentum of the tennis ball:
Momentum_ball_initial = Mass_ball × Speed_ball_initial
Momentum_ball_initial = 0.057 kg × 72.0 m/s
Momentum_ball_initial = 4.104 kg·m/s
3. Use the conservation of momentum principle to find the final momentum of the tennis ball:
Momentum_ball_final = Momentum_ball_initial
Momentum_ball_final = 4.104 kg·m/s
4. Use the momentum equation to find the final speed of the tennis ball:
Momentum_ball_final = Mass_ball × Speed_ball_final
4.104 kg·m/s = 0.057 kg × Speed_ball_final
Speed_ball_final = 4.104 kg·m/s ÷ 0.057 kg
Speed_ball_final = 72.0 m/s
5. Since the tennis ball is traveling in the reverse direction after the collision, the speed of the player's center of mass just after hitting the ball will also be 72.0 m/s, but in the opposite direction.
Therefore, the speed of the tennis player's center of mass just after hitting the ball will be 72.0 m/s in the opposite direction.
To find the speed of the tennis player's center of mass just after hitting the ball, we need to apply the law of conservation of linear momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, provided no external forces act on the system.
In this scenario, the initial momentum is only due to the tennis ball, as the tennis player is initially at rest. The momentum of an object is given by the product of its mass and velocity.
Initial momentum of the system = mass of the tennis ball × velocity of the tennis ball
Given:
Mass of the tennis ball (m₁) = 57.0 g = 0.057 kg
Velocity of the tennis ball (v₁) = 72.0 m/s
Initial momentum of the system = 0.057 kg × 72.0 m/s = 4.104 kg·m/s (in the positive direction)
After the tennis player hits the ball, the ball will reverse its direction with a new velocity of 48.0 m/s. This change in momentum should be balanced by the opposite change in momentum of the tennis player.
Final momentum of the system = (− mass of the tennis ball) × (− velocity of the tennis ball) + mass of the tennis player × (− velocity of the tennis player)
Let's assume the final momentum is in the negative direction.
Final momentum of the system = (−0.057 kg) × (−48.0 m/s) + (55.0 kg) × (−velocity of the player)
Since the final momentum should be equal to the initial momentum:
4.104 kg·m/s = 0.057 kg × 48.0 m/s + 55.0 kg × (−velocity of the player)
Simplifying the equation:
4.104 kg·m/s = 2.736 kg·m/s − 55.0 kg × velocity of the player
Rearranging to solve for velocity of the player:
55.0 kg × velocity of the player = 4.104 kg·m/s − 2.736 kg·m/s
55.0 kg × velocity of the player = 1.368 kg·m/s
Dividing both sides by 55.0 kg:
velocity of the player = 1.368 kg·m/s ÷ 55.0 kg
velocity of the player = 0.0249 m/s (approx)
Therefore, just after hitting the ball, the tennis player's center of mass will be moving horizontally at a speed of approximately 0.0249 m/s.