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

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

Step-by-step 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+(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=√(2gh_m)`

`v_o=√(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=(v_o)/(g)`

`\displaystyle t_m=(39)/(9.8)`

`t_m=4\ s`