Answer:
e) 120m/s
Explanation:
When the ball reaches its highest point, its velocity becomes zero, meaning
.
where
is the initial velocity.
Solving for
we get
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
since it had reached the highest point, the ball has traveled downwards and the velocity
it has gained is
,
and we are told that this is twice the initial velocity
; therefore,
![v_f = 2v_0 = gt_0](https://tex.z-dn.net/?f=v_f%20%3D%202v_0%20%20%3D%20gt_0)
which gives
![t_0 = \dfrac{2v_0}{g}.](https://tex.z-dn.net/?f=t_0%20%3D%20%5Cdfrac%7B2v_0%7D%7Bg%7D.)
Thus, the total time taken to reach velocity
is
![t_{tot} = t+t_0 = \dfrac{v_0}{g}+\dfrac{2v_0}{g}](https://tex.z-dn.net/?f=t_%7Btot%7D%20%3D%20t%2Bt_0%20%3D%20%5Cdfrac%7Bv_0%7D%7Bg%7D%2B%5Cdfrac%7B2v_0%7D%7Bg%7D)
![t_{tot} = \dfrac{3v_0}{g}.](https://tex.z-dn.net/?f=t_%7Btot%7D%20%3D%20%5Cdfrac%7B3v_0%7D%7Bg%7D.)
This
, we are told, is 36 seconds; therefore,
![36= \dfrac{3v_0}{g},](https://tex.z-dn.net/?f=36%3D%20%5Cdfrac%7B3v_0%7D%7Bg%7D%2C)
and solving for
we get:
![v_0 = \dfrac{36g}{3}](https://tex.z-dn.net/?f=v_0%20%3D%20%5Cdfrac%7B36g%7D%7B3%7D)
![v_0 = \dfrac{36s(10m/s^2)}{3}](https://tex.z-dn.net/?f=v_0%20%3D%20%5Cdfrac%7B36s%2810m%2Fs%5E2%29%7D%7B3%7D)
![\boxed{v_0 = 120m/s}](https://tex.z-dn.net/?f=%5Cboxed%7Bv_0%20%3D%20120m%2Fs%7D)
which from the options given is choice e.
b is the answer there you go if you need the answer
True. Think of a magnet and how they only connect to the opposite charges.