Answer to Question #265520 in Mechanical Engineering for nawras

Question

Problem 1 Stone A is hurled vertically upwards from a tower of height h with a speed vA0. Simultaneously, stone B is thrown vertically upwards from the ground with a speed of vB0. Given: h = 30 m ; vA0 = 15 m/s ; vB0 = 25 m/s ; g = 9.81 m/s 2 Find: 1. At which height and time do the stones fly past another? 2. At this time, what is the speed of stone A relative to stone B? 3. Draw the following diagrams: acceleration-time, speed-time and distance-time.Problem 2 In the system pictured below, point B slides with velocity vሬ⃗஻. Given: β, , vሬ⃗஻ Find: The velocity vሬ⃗஼ of point C by calculation

Answer 1

At which height do the stones fly past another.

$v_a² = u_a²-2gs\\ 0² = 15² -2(g)(H+30)\\ 0 = 225 -2g(H+30)\\ g = 225/2(H+30)\ --(i)\\ v_b² = u_b²-2gH\\ 0²= 25²-2(g)H\\ 0 = 625 -2gH\\ g =625/2H\ --(ii)$

substituting equation (ii) into equation (i)

$225/2(H+30) = 625/2H\\ 9/(H+30) = 25/H\\ 9H = 25(H+30)\\ 9H = 25H + 750\\ 16H = 750\\ H = 46.88\textsf{ m}$