finding expression in time

Question

An archer fires an arrow straight up into the air with a speed Vo = 14 m/s. Neglect air resistance.

Write an expression for the time the arrow is in the air until it returns to launch height in terms of known quantities.

Answer 1

We use

Vf = Vi +at

Vf = 0 for upward motion

Vi = 14m/s

a = -g

So 0 =14 -gt

so t= 14/g m/s

Same will be time for downward motion due to symmetry

So total time = T = 2t = 28/g Sec

Plug in g= 9.81 m/s2

Hence

T = 28/9.81 sec

So Expression for time is

T = 2 V₀ /g