A racquet ball with mass m = 0.224 kg is moving toward the wall at v = 14.8 m/s and at an angle of è = 27° with respect to the horizontal. The ball makes a perfectly elastic collision with the solid, frictionless wall and rebounds at the same angle with respect to the horizontal. The ball is in contact with the wall for t = 0.077s.
What is the magnitude of the change in momentum of the racquet ball?
(0.224 kg)(14.8 m/s)*cos(27°)
=2.954 kg*m/s
The change in momentum is -2*2.954 kg*m/s, so the magnitude of the change is 5.91 kg*m/s.
To find the magnitude of the change in momentum of the racquet ball, we need to first find the initial momentum and final momentum, and then calculate the difference.
1. Find the initial momentum:
The initial momentum (p_initial) of the ball can be calculated using the formula:
p_initial = m * v_initial
where:
m = mass of the racquet ball (0.224 kg)
v_initial = initial velocity of the ball before collision
Since the ball is moving at an angle of è = 27° with respect to the horizontal, we need to find the horizontal and vertical components of its velocity.
Horizontal component of velocity:
v_initial_horizontal = v_initial * cos(è)
Vertical component of velocity:
v_initial_vertical = v_initial * sin(è)
Given:
v = 14.8 m/s (initial velocity)
è = 27° (launch angle)
Using these values, we can calculate the initial horizontal and vertical components of velocity:
v_initial_horizontal = 14.8 * cos(27°)
v_initial_vertical = 14.8 * sin(27°)
2. Find the final momentum:
Since the collision is perfectly elastic, the magnitude of velocity after rebounding will be the same. So, the final momentum (p_final) can be calculated using the formula:
p_final = m * v_final
where:
v_final = final velocity of the ball after collision
Using the same logic as before, we can calculate the final horizontal and vertical components of velocity (v_final_horizontal and v_final_vertical):
v_final_horizontal = v * cos(è)
v_final_vertical = v * sin(è)
3. Calculate the change in momentum:
The change in momentum (Δp) can be calculated using the formula:
Δp = p_final - p_initial
Now, we have the components of initial and final momentum. We can calculate the change in momentum by finding the difference between the final and initial momentum.
Δp_horizontal = m * (v_final_horizontal - v_initial_horizontal)
Δp_vertical = m * (v_final_vertical - v_initial_vertical)
Finally, we can calculate the magnitude of the change in momentum using the Pythagorean theorem:
magnitude of Δp = sqrt((Δp_horizontal)^2 + (Δp_vertical)^2)
By substituting the calculated values into these equations, we can find the magnitude of the change in momentum of the racquet ball.