Question

A balloon moves up vertically such that if a stone is projected with a horizontal velocity u relative to balloon, the ​stone always hits the ground at a fixed point at a distance (2u 2 /g) ​horizontally away from it. Find the height of the​ ​balloon as a function of time.

Answer 1

R = 2 u^2 / g
let the height be = h

time to drop onto the ground = t
h(t) = 1/2 g t^2
t = √[2 h(t) / g]
R = u * t = u √[2 h(t)/g ]  = 2 u² / g   given

h (t) = 2 u² / g

The height is constant at the above value.