Calculate the speed at which the bullet leaves the rifle using the principle of conservation of momentum.

Step 1: Calculate the speed at which the bullet leaves the rifle using the principle of conservation of momentum. Let m_b be the mass of the bullet, m_r be the mass of the rifle. Let u_b and u_r be their initial velocities, and v_b and v_r be their final velocities. Given: m_b = 20 g = 0.020 kg m_r = 3 kg u_b = 0 m/s (rifle is stationary) u_r = 0 m/s (rifle is stationary) v_r = -1.4 m/s (recoils, so opposite direction to bullet) According to the conservation of momentum: m_b u_b + m_r u_r = m_b v_b + m_r v_r (0.020 kg)(0 m/s) + (3 kg)(0 m/s) = (0.020 kg) v_b + (3 kg)(-1.4 m/s) 0 = 0.020 v_b - 4.2 0.020 v_b = 4.2 v_b = (4.2)/(0.020) v_b = 210 m/s The speed at which the bullet leaves the rifle is the magnitude of v_b. The speed is 210 m/s Step 2: Calculate the magnitude of the average force exerted by the block on the bullet. The bullet enters the block with the speed calculated in Step 1 and comes to rest. Given: Mass of bullet m_b = 0.020 kg Initial velocity of bullet u = 210 m/s Final velocity of bullet v = 0 m/s Distance travelled s = 0.4 m First, calculate the acceleration (a) of the bullet using a kinematic equation: v^2 = u^2 + 2as (0 m/s)^2 = (210 m/s)^2 + 2a(0.4 m) 0 = 44100 + 0.8a 0.8a = -44100 a = (-44100)/(0.8) a = -55125 m/s^2 The negative sign indicates deceleration. Next, calculate the average force (F) using Newton's Second Law: F = m_b a F = (0.020 kg)(-55125 m/s^2) F = -1102.5 N The magnitude of the average force is the absolute value of F. The magnitude of the average force exerted by the block on the bullet is 1102.5 N Step 3: Compare the magnitude of the force calculated in QUESTION 4.2 to the magnitude of the force exerted by the bullet on the block. According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. The force exerted by the block on the bullet and the force exerted by the bullet on the block are an action-reaction pair. Therefore, their magnitudes are equal. The magnitude of the force calculated in QUESTION 4.2 compared to the magnitude of the force exerted by the bullet on the block is THE SAME