Question

do all please.

1. A 20 Kg cart moving at 10 m/s collides with a 10 Kg cart moving at 20 m/ s. The two carts stick to each other after the collision. Calculate the final speed of the carts just after the collision if () They were moving in the same direction direction (i.e. thefaster bumped the slower from behind) (ii) They were moving at 90° respect to each other. (ii) They were moving at 30° respect to each other 30°

Answer 1

m_1 = 20 kg m_2 = 10 kg v_1 = 10 m/s v_2 = 20 m/s (i) If they are moving in same direction By momentum conservation P_i = P_f 20 times 10 + 10 times 20 = 30 times V therefoe V = 40/3 m/s (ii) Moving perpendicular to each other Velocity after collision V = V_x i + V_y j Momentum conservation in both direction 20 times 10 = 30 V_x V_x = 20/3 m/s \r\n 20 times 10 = 30 V_y V_y = 20/3 m/s speed = Vertical-bar v Vertical-bar = squareroot V_x^2 + V_y^2 = squareroot 2 times 400/9 = 20/3 squareroot 2 = 9.428 m/sec (iii) Final velocity V = V_x i + V_y j In x-direction momentum conservation 20 times 10 + 10 times 10 squareroot 3 = 30 V_x 100 (2 + squareroot 3) = 30 V_x therefore V_x = 10/3 (2 + squareroot 3) = 12.44 m/s