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?
This question was asked and answered yesterday. Just use conservation of momentum, as I explained earlier. I explained it all the way to the next-to-last step.
Our teachers will gladly show you how to do problems such as this, but not do them for you in their entirety.
To determine how fast the center of mass of the tennis player will be moving horizontally just after hitting the ball, we need to consider the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act upon it. In this case, the tennis player and the tennis ball can be considered as an isolated system, as no external forces are mentioned.
First, let's calculate the momentum of the tennis player and the tennis ball before the collision. The momentum of an object is given by its mass multiplied by its velocity.
Momentum before collision = mass × velocity
The momentum of the tennis player (m1) before the collision:
m1 = 55.0 kg (mass of the tennis player)
v1 = 0 m/s (as the tennis player is not moving horizontally before hitting the ball)
Momentum of the tennis player before the collision = m1 × v1 = 55.0 kg × 0 m/s = 0 kg·m/s
The momentum of the tennis ball (m2) before the collision:
m2 = 57.0 g = 0.057 kg (mass of the tennis ball)
v2 = 72.0 m/s (horizontal velocity of the tennis ball)
Momentum of the tennis ball before the collision = m2 × v2 = 0.057 kg × 72.0 m/s = 4.104 kg·m/s
Since momentum is conserved, the total momentum before the collision is equal to the total momentum after the collision.
Total momentum before collision = Total momentum after collision
0 kg·m/s + 4.104 kg·m/s = Total momentum after collision
Now, let's calculate the momentum of the tennis player and the tennis ball after the collision. The momentum of the tennis player after the collision will depend on the change in the ball's momentum.
The momentum of the tennis player (m1) after the collision:
v1' = ? (velocity of the tennis player after the collision)
The momentum of the tennis ball (m2) after the collision:
v2' = -48.0 m/s (since the ball is traveling in the reverse direction)
Total momentum after the collision = m1 × v1' + m2 × v2'
Now, we can solve the equation:
0 kg·m/s + 4.104 kg·m/s = (55.0 kg) × v1' + (0.057 kg) × (-48.0 m/s)
4.104 kg·m/s = 55.0 kg × v1' - 2.736 kg·m/s
Let's rearrange the equation to solve for v1':
v1' = (4.104 kg·m/s + 2.736 kg·m/s) / 55.0 kg
v1' = 6.84 kg·m/s / 55.0 kg
v1' = 0.124 m/s
Therefore, the center of mass of the tennis player will be moving horizontally at a speed of 0.124 m/s just after hitting the ball.