A 0.3 kg brick is dropped form a height of 8 meters. It hits the ground and comes to rest.

a) Calculate the impulse exerted by ground on the brick.
b) It takes 0.0013 seconds from the time the brick first touches the ground until it touches the ground. Calculate the average force exerted by the ground on the brick.

To answer this question, we need to use the principles of impulse and momentum. Impulse is the change in momentum of an object and is calculated using the equation: Impulse = Change in momentum = Final momentum - Initial momentum.

a) To calculate the impulse exerted by the ground on the brick, we need to find the change in momentum. The momentum of an object is given by the equation: momentum = mass × velocity.

Given:
- Mass of the brick (m) = 0.3 kg
- Height from which the brick is dropped (h) = 8 meters

First, we need to find the initial velocity (u) of the brick when it hits the ground. Since the brick is dropped from rest, its initial velocity is 0 m/s.

Next, we need to find the final velocity (v) of the brick just before it hits the ground. We can use the equation of motion: v^2 = u^2 + 2gh, where g is the acceleration due to gravity (approximately 9.8 m/s^2).

Using this equation:
v^2 = 0^2 + 2 × 9.8 × 8
v^2 = 156.8
v ≈ √156.8
v ≈ 12.53 m/s

Now, we can calculate the initial momentum (P_initial) and the final momentum (P_final) of the brick.

P_initial = mass × initial velocity
P_initial = 0.3 kg × 0 m/s
P_initial = 0 kg·m/s

P_final = mass × final velocity
P_final = 0.3 kg × (12.53 m/s)
P_final ≈ 3.76 kg·m/s

Finally, we can calculate the impulse (J) exerted by the ground on the brick.

Impulse (J) = Change in momentum = P_final - P_initial
J = 3.76 kg·m/s - 0 kg·m/s
J ≈ 3.76 kg·m/s

Therefore, the impulse exerted by the ground on the brick is approximately 3.76 kg·m/s.

b) To calculate the average force exerted by the ground on the brick, we can use the equation: Average force = Impulse / Time.

Given:
- Time (t) = 0.0013 seconds

Using the impulse calculated in part a):

Average force = Impulse / Time
Average force = 3.76 kg·m/s / 0.0013 s
Average force ≈ 2892.31 N

Therefore, the average force exerted by the ground on the brick is approximately 2892.31 Newtons.