1 Calculate the man's speed just before he grabs the boy. Ignore the effects of friction. 6.2 Is the collision elastic? Use a calculation to support your answer.

Hey, good to see you again. 6.1 Calculate the man's speed just before he grabs the boy. Ignore the effects of friction. Step 1: Identify the given values. Mass of man, m_m = 87 kg Mass of boy, m_b = 22 kg Initial velocity of boy, v_b,i = 0 m/s (standing still) Final velocity of man and boy together, v_f = 2.4 m/s Step 2: Apply the principle of conservation of momentum for a perfectly inelastic collision. The total momentum before the collision equals the total momentum after the collision. m_m v_m,i + m_b v_b,i = (m_m + m_b) v_f Step 3: Substitute the known values into the equation. (87 kg) v_m,i + (22 kg)(0 m/s) = (87 kg + 22 kg)(2.4 m/s) 87 v_m,i = (109 kg)(2.4 m/s) 87 v_m,i = 261.6 kg · m/s Step 4: Solve for v_m,i. v_m,i = 261.6 kg · m/s87 kg v_m,i = 3.00689... m/s Rounding to two decimal places: v_m,i = 3.01 m/s The man's speed just before he grabs the boy is 3.01 m/s. 6.2 Is the collision elastic? Use a calculation to support your answer. Step 1: Calculate the total kinetic energy before the collision (KE_i). KE_i = (1)/(2) m_m v_m,i^2 + (1)/(2) m_b v_b,i^2 Using v_m,i = 3.00689... m/s from the previous calculation for accuracy: KE_i = (1)/(2) (87 kg) (3.00689... m/s)^2 + (1)/(2) (22 kg) (0 m/s)^2 KE_i = (1)/(2) (87 kg) (9.0414 m^2/s^2) + 0 KE_i = 393.29 J Step 2: Calculate the total kinetic energy after the collision (KE_f). KE_f = (1)/(2) (m_m + m_b) v_f^2 KE_f = (1)/(2) (87 kg + 22 kg) (2.4 m/s)^2 KE_f = (1)/(2) (109 kg) (5.76 m^2/s^2) KE_f = 313.92 J Step 3: Compare the initial and final kinetic energies. KE_i = 393.29 J KE_f = 313.92 J Since KE_i ≠ KE_f, kinetic energy is not conserved. Step 4: Conclude whether the collision is elastic. The collision is not elastic because the total kinetic energy before the collision (393.29 J) is not equal to the total kinetic energy after the collision (313.92 J). This is characteristic of an inelastic collision. 6.3 Calculate the magnitude of the force exerted by the gravel surface on the man and the boy. Step 1: Identify the known values for the motion on the gravel surface. Combined mass, M = m_m + m_b = 87 kg + 22 kg = 109 kg Initial velocity on gravel, v_i' = 2.4 m/s (this is v_f from the collision) Final velocity on gravel, v_f' = 0 m/s (comes to rest) Distance traveled on gravel, d = 2 m Step 2: Calculate the acceleration (a) using a kinematic equation. v_f'^2 = v_i'^2 + 2ad (0 m/s)^2 = (2.4 m/s)^2 + 2a(2 m) 0 = 5.76 m^2/s^2 + 4a m -4a m = 5.76 m^2/s^2 a = 5.76 m^2/s^2-4 m a = -1.44 m/s^2 The negative sign indicates deceleration. Step 3: Calculate the magnitude of the force using Newton's second law (F = Ma). F = M |a| F = (109 kg) (1.44 m/s^2) F = 156.96 N The magnitude of the force exerted by the gravel surface is 157.0 N. Send me the next one 📸