Question

An object is thrown upward with some velocity. If the object rises 77.5 m above the point of release, (a) how fast was the object thrown?, (b) How long did it take for the object to reach it's highest point ?

Answer 1

Answer:

$v_o=39\ m/s\\t_m=4\ s$

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:

$\displaystyle h_m=H+\frac{v_o^2}{2g}$

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:

$\displaystyle v_o=\sqrt{2gh_m}$

$v_o=\sqrt{2\cdot 9.8\cdot 77.5}$

$v_o=39\ m/s$

(b)

The maximum time or the time taken by the object to reach its highest  point is calculated as follows:

$\displaystyle t_m=\frac{v_o}{g}$

$\displaystyle t_m=\frac{39}{9.8}$

$t_m=4\ s$