Question

After solving a difficult physics problem, an excited student throws his book straight up. It leaves his hand at 3.9 m/s from 1.5 m above the ground. (a) How much time Moes it take until the book hits the floor? (b) What's its velocity then? 

Answer 1

given

u = 3.9 m/sec

S_o = 1.5 m

using equation

S = S_o + u t + 1/2 a t²

after some time the book hits the floor at S = 0

0 = 1.5 + 3.9 t - 1/2 x 9.8 x t²

4.9 t² - 3.9 t - 1.5 = 0

by solving the quadratic equation we get

t = 0.864 sec

b )

book reaches its maximum height t = t_max , at that the velocity is zero

so u - a t_max = 0

t_max = 0.255 sec

the final velocity is V_f = a ( t_max - t)

= 5.97 m/sec