Answer:
[tex]v_o=39\ m/s\\t_m=4\ s[/tex]
Explanation:
Vertical Launch Upwards
In a vertical launch upwards, an object is launched vertically up from a height H without taking into consideration any kind of friction with the air.
If vo is the initial speed and g is the acceleration of gravity, the maximum height reached by the object is given by:
[tex]\displaystyle h_m=H+\frac{v_o^2}{2g}[/tex]
The object referred to in the question is thrown from a height H=0 and the maximum height is hm=77.5 m.
(a)
To find the initial speed we solve for vo:
[tex]\displaystyle v_o=\sqrt{2gh_m}[/tex]
[tex]v_o=\sqrt{2\cdot 9.8\cdot 77.5}[/tex]
[tex]v_o=39\ m/s[/tex]
(b)
The maximum time or the time taken by the object to reach its highest point is calculated as follows:
[tex]\displaystyle t_m=\frac{v_o}{g}[/tex]
[tex]\displaystyle t_m=\frac{39}{9.8}[/tex]
[tex]t_m=4\ s[/tex]
