Question

the horizontal drift of the balloon x (y).

Answer 1

Given that vertical velocity of the balloon $\frac{dy}{dt}=v_o$ ..(1)

Horizontal velocity component $\frac{dx}{dt}=ky$ ....(2)

On dividing 1 and 2 we get

$\frac{dy}{dx}=\frac{v_o}{ky}$

$⟹$ $dx=\frac{ky}{v_o}dy$

On integration we get $\int dx=\frac{k}{v_o}\int ydy$

$⟹$ Horizontal drift $x=\frac{k}{v_o}\frac{y^2}{2}$