Answer:
e) 120m/s
Explanation:
When the ball reaches its highest point, its velocity becomes zero, meaning
[tex]v_0-gt = 0[/tex].
where [tex]v_0[/tex] is the initial velocity.
Solving for [tex]t[/tex] we get
[tex]t = \dfrac{v_0}{g}[/tex]
which is the time it takes the ball to reach the highest point.
Now, after the ball has reached its highest point, it turns around and falls downwards. After time [tex]t_0[/tex] since it had reached the highest point, the ball has traveled downwards and the velocity [tex]v_f[/tex] it has gained is
[tex]v_f = gt_0[/tex],
and we are told that this is twice the initial velocity [tex]v_0[/tex]; therefore,
[tex]v_f = 2v_0 = gt_0[/tex]
which gives
[tex]t_0 = \dfrac{2v_0}{g}.[/tex]
Thus, the total time taken to reach velocity [tex]2v_0[/tex] is
[tex]t_{tot} = t+t_0 = \dfrac{v_0}{g}+\dfrac{2v_0}{g}[/tex]
[tex]t_{tot} = \dfrac{3v_0}{g}.[/tex]
This [tex]t_{tot}[/tex], we are told, is 36 seconds; therefore,
[tex]36= \dfrac{3v_0}{g},[/tex]
and solving for [tex]v_0[/tex] we get:
[tex]v_0 = \dfrac{36g}{3}[/tex]
[tex]v_0 = \dfrac{36s(10m/s^2)}{3}[/tex]
[tex]\boxed{v_0 = 120m/s}[/tex]
which from the options given is choice e.
