Final answer:
To find the average force exerted by the wall on the ball, use the impulse-momentum principle. First, find the initial momentum of the ball using its mass and initial velocity. Then find the final momentum of the ball using its mass, final velocity, and direction of motion. Finally, calculate the change in momentum and divide it by the time of contact to find the average force exerted by the wall. The average force exerted by the wall on the ball is -259.8 N.
Step-by-step explanation:
To find the average force exerted by the wall on the ball, we need to use the impulse-momentum principle. The impulse experienced by the ball is equal to the change in momentum of the ball. The initial momentum of the ball before the collision with the wall can be found using the mass of the ball and its initial velocity. The final momentum of the ball after the collision can be found using the mass of the ball, its final velocity, and the direction of motion. The difference between the two momenta gives us the change in momentum, which can be divided by the time of contact to find the average force exerted by the wall on the ball.
First, let's find the initial momentum of the ball. The initial velocity of the ball can be split into its x and y components using the given angle. The x-component is found by multiplying the initial velocity by the cosine of the angle, while the y-component is found by multiplying the initial velocity by the sine of the angle. Since the ball moves in a vertical direction, the x-component of the initial velocity is 0. The y-component can be found as follows:
y-component of initial velocity = 10 m/s * sin(60)
y-component of initial velocity = 10 m/s * 0.866
y-component of initial velocity = 8.66 m/s
The initial momentum of the ball is the product of its mass and its y-component of initial velocity:
Initial momentum = 3.00 kg * 8.66 m/s
Initial momentum = 25.98 kg·m/s
Next, let's find the final momentum of the ball. The final velocity of the ball after the collision has the same magnitude as the initial velocity but in the opposite direction. The x-component of the final velocity is 0, and the y-component can be found in the same way as the initial velocity:
y-component of final velocity = 10 m/s * sin(-60)
y-component of final velocity = 10 m/s * -0.866
y-component of final velocity = -8.66 m/s
The final momentum of the ball is the product of its mass and its y-component of final velocity:
Final momentum = 3.00 kg * -8.66 m/s
Final momentum = -25.98 kg·m/s
Finally, we can calculate the change in momentum by subtracting the initial momentum from the final momentum:
Change in momentum = -25.98 kg·m/s - 25.98 kg·m/s
Change in momentum = -51.96 kg·m/s
Since the momentum change occurs over a time of 0.200 s, we can find the average force exerted by the wall on the ball by dividing the change in momentum by the time of contact:
Average force = Change in momentum / Time
Average force = -51.96 kg·m/s / 0.200 s
Average force = -259.8 N
Therefore, the average force exerted by the wall on the ball is -259.8 N.