Question

The instantaneous height $y$ of a projectile and the distance covered $x$ , are as follows, $x=5t$ , $y=5t-2t^2$ . What is the acceleration due to gravity if distance is measured in meters and time in seconds.

Answer 1

Here, the acceleration due to gravity affect the vertical height only.

$y=5t-2t^2$

The instantaneous velocity in the vertical direction is,

$\frac{dy}{dt}=5-4t$

The instantaneous acceleration in the vertical direction is,

$\frac{d^{2}y}{d{t}^2}=-4$

Thus, the acceleration due to gravity is $g=4m/s^2$.