Final answer:
The magnitude of the constant force acting on the rock can be determined by calculating the rock's initial velocity upon hitting the ground, the velocity with which it leaves the ground after bouncing, the change in momentum using these velocities, and then dividing by the contact time with the ground.
Step-by-step explanation:
To determine the magnitude of the constant force f acting on the rock when it hit the ground, we will use the concept of impulse, which is the product of force and the time over which the force acts, and is equal to the change in momentum (mass times change in velocity).
Firstly, we find the initial velocity of the rock just before it hits the ground using the equation for the final velocity in free fall: v^2 = u^2 + 2gh, where v is the final velocity, u = 0 (since the rock is dropped from rest), g is the acceleration due to gravity (9.81 m/s^2), and h is the height (3.65 m). Similarly, we calculate the velocity with which the rock leaves the ground after bouncing to reach a height of 2.49 m.
Next, we use the impulse-momentum theorem: Impulse = ΔP = m(v_final - v_initial). Since the rock comes to a brief stop when in contact with the ground, the initial velocity for the impulse calculation after the bounce will be 0 m/s. We calculate the change in the rock's momentum and then divide it by the contact time t = 0.124 s to find the average force.
To calculate the actual numerical values, you would use the steps outlined above and substitute the appropriate numbers. Remember that the velocity after the bounce is directed upwards (positive), while the initial velocity just before impact is downwards (negative), so they should be treated as vectors when calculating the change in momentum.