Aprojectile is fired straight upward with an initial veloc- ity of 100 m=s from the top of a building 20 m high and falls to the ground at the base of the building. find (a) its maximum height above the ground; (b) when it passes the top of the building; (c) its total time in the air.

The answer to your question is:

a) h max = 529.7 m

b) t = 20.4 s

c) t = 20.6 s

Explanation:

a) h max = -(vo)² / 2g

              = 100² / 2(9.81)

              = 10000 / 19.62

              = 509.7 m

total height = 509.7 + 20 = 529.7 m

b)  

    h = gt² / 2

    t = √ 2h / g

    t = √ 2(509.7)/9.81

    t = √ 103.91

    t = 10.19 s  

    total time = 2 x t = 2 x 10.19 = 20.4 s

c)

   h = vot + 1/2gt²

   20 = 100t + 1/2(9.91) t²

  4.9t² + 100 t -20 = 0   quadratic equation

t = 0.19 s

Total time = 0.19 + 20.4 = 20.6 s