Answer:
The height is 80 meters.
Explanation:
The equation for the distance in the second segment of the fall is as below. In it, we use the initial velocity v1 that the ball had after completing the first segment. From this equation, v1 can be determined:
[tex]h_2 = \frac{1}{2}gt_2^2+v_1t_2=0.5\cdot 10\frac{m}{s^2}\cdot 4 s^2+v_1\cdot 2 s=60m\implies\\v_1 = 20\frac{m}{s}[/tex]
Next, we use the kinematic equation for velocity at the end of the first segment of a free fall, to determine h1:
[tex]v_1^2 = 2gh_1+v_0^2 = 2gh_1\implies h_1 = \frac{v_1^2}{2g}=20m[/tex]
The total height is then
[tex]h = h_1 + h_2 = 20m + 60 m = 80m[/tex]
