Question

If a stone projected from ground ,takes 4 s to reach the topmost point of its trajectory ,then time of flight is

Answer 1

you project a stone from the ground and it takes 4 s to reach topmost point of its trajectory. Let stone reach H height above from the ground. at topmost point, velocity = 0

so, final velocity, v = 0
Let initial velocity is u
then, use formula v = u + at
0 = u + (-g) × 4
u = 40 m/s
hence, initial velocity = 40 m/s

Height , H = u²/2g
= (40)²/2 × 10 = 1600/20 = 80 m

now time taken to fall the stone = t'
initial velocity at top point = 0
so, S = ut + 1/2 at²
-80 = 0 - 1/2 × 10 × t²
-160 = -10t² => t = 4 s

$\textbf{hence , time of flight = 4 + 4 = 8sec}$