A hockey goalie is standing on ice. Another player fires a puck (m = 0.22 kg) at the goalie with a velocity of +63 m/s

(a) If the goalie catches the puck with his glove in a time of 7.0 10-3 s, what is the average force (magnitude and direction) exerted on the goalie by the puck?
N

(b) Instead of catching the puck, the goalie slaps it with his stick and returns the puck straight back to the player with a velocity of +63 m/s. The puck and stick are in contact for a time of 7.0 10-3 s. Now what is the average force exerted on the goalie by the puck?
N

To solve this problem, we can use Newton's second law, which states that the force exerted on an object is equal to the rate of change of its momentum. The equation for this is F = Δp/Δt, where F is the force, Δp (change in momentum) is the final momentum minus the initial momentum, and Δt is the change in time.

(a) To find the average force exerted on the goalie by the puck when caught with the glove, we need to calculate the change in momentum and divide it by the time taken to catch the puck.

1. Find the initial momentum (p_initial) of the puck using the equation p_initial = m * v_initial, where m is the mass of the puck and v_initial is the initial velocity of the puck.
p_initial = 0.22 kg * 63 m/s = 13.86 kg·m/s

2. Find the final momentum (p_final) of the puck using the equation p_final = m * v_final, where v_final is the final velocity of the puck.
Since the puck is caught with the glove and comes to rest, the final velocity is 0 m/s.
p_final = 0.22 kg * 0 m/s = 0 kg·m/s

3. Calculate the change in momentum (Δp) by subtracting the initial momentum from the final momentum.
Δp = p_final - p_initial = 0 kg·m/s - 13.86 kg·m/s = -13.86 kg·m/s

4. Now, divide the change in momentum by the time taken to catch the puck (Δt = 7.0 × 10^(-3) s) to find the average force.
F = Δp/Δt = (-13.86 kg·m/s) / (7.0 × 10^(-3) s)

You can calculate the magnitude and direction of this force using the given values. The magnitude will be a positive value, indicating the force exerted on the goalie by the puck. The direction of the force will be in the opposite direction of the initial velocity of the puck (+63 m/s).

(b) To find the average force exerted on the goalie by the puck when slapping it back with the stick, we can use the same formula and steps as in part (a), but with different initial and final velocities.

1. Find the initial momentum (p_initial) of the puck using the equation p_initial = m * v_initial, where m is the mass of the puck and v_initial is the initial velocity of the puck.
The initial velocity is +63 m/s, so using the given values:
p_initial = 0.22 kg * (+63 m/s) = 13.86 kg·m/s

2. Find the final momentum (p_final) of the puck. Since the puck is slapped back with the stick and returns to the player with the same velocity (+63 m/s), the final momentum will also be the same.
p_final = 0.22 kg * (+63 m/s) = 13.86 kg·m/s

3. Calculate the change in momentum (Δp) by subtracting the initial momentum from the final momentum.
Δp = p_final - p_initial = 13.86 kg·m/s - 13.86 kg·m/s = 0 kg·m/s

4. Now, divide the change in momentum by the time during which the puck and stick are in contact (Δt = 7.0 × 10^(-3) s) to find the average force.
F = Δp/Δt = (0 kg·m/s) / (7.0 × 10^(-3) s)

Again, you can calculate the magnitude and direction of this force using the given values. The magnitude will be zero, indicating that no net force is exerted on the goalie by the puck when it is slapped back with the stick.