Question

A ball is thrown vertically upward, which is the positive direction. a little later it returns to its point of release. the ball is in the air for a total time of 8.14 s. what is its initial velocity? neglect air resistance.

Answer 1

This motion of all can be divided in to two, first the upward motion and second downward motion.

In case of projectiles time taken for upward motion = time taken for downward motion.

So we have time taken for upward motion = 8.14/2 = 4.07 seconds

We have equation of motion, v = u+at, where v is the final velocity , u is the initial velocity, a is the acceleration and t is the time taken.

In case of upward motion

    v = 0 m/s

    t = 4.07 seconds

    a = -9.8 $m/s^2$

  Substituting

       $0 = u - 9.8*4.07\\ \\ u = 39.886 m/s$

So initial velocity of ball = 39.886 m/s.