QUIZ 2

1. A ball is thrown horizontally from the top of a building 35m high. The ball strikes the ground at a point 80m from the base of the building. Find (a) the time the ball is in flight, (b) its initial velocity, and (c) the x and y components of velocity just before the ball strikes the ground.

Answer. We resolve the motion into x and y components

               vx = v0,   v0y = 0

             (a) We find the time from vertical motion

               y = y0 + 1/2ayt2;

              0  = (35m) + 1/2(-9.80m/s2)t2,   which gives t = 2.67s.

             (b) v0 = vx = x/t = 80m/2.67s = 29.96m/s

             (c) When the ball strikes the ground, we find

                   vy = ayt = (-9.80m/s2)(2.67s) = 26.17m/s,       vx = 29.96m/s.

 

 2. Two unequal masses are attached by a lightweight string that passes over a frictionless pulley of negligible mass as in Figure. The block of mass m2 lies on a frictionless incline of angle q. Find the magnitude of the acceleration of the two masses and the tension in the string.

Solution. The free-body diagrams are as shown.

              For mass m1 we write SF = ma

                    x-component: SFx = 0

                    y-component: T - m1g = m1a

             For mass m2 we write

                   x-component: m2gsinq - T = m2a

                   y-component: FN - m2gcosq = 0

           Solving the four equations, we get

                  a = (m2gsinq - m1g)/(m1 + m2)

                 T = m1m2g(1 + sinq)/(m1 + m2)