Answer to Question #105560 in Algebra for Thomas Baraka

Question

A stone is dropped from a height (h) above the ground. It strikes the ground t seconds later.show that acceleration due to gravity is given by g=2h/t×t

Answer 1

An object is said to be a freely falling body if it is thrown or dropped vertically at an initial velocity and then only gravity affects its motion.

The position of any freely falling body is determined by the initial velocity $v_0$ and the initial height $h.$

The model for height of a falling object is: 

$$y(t)=h+v_0t-{gt^2 \over 2}$$

Assume that $v_0=0.$ Then

$$y(t)=h-{gt^2 \over 2}$$

A stone strikes the ground $t_1$ t seconds later

$$y(t_1)=0=>h-{gt_1^2 \over 2}=0$$

Solve for $g$

$$g={2h \over t_1^2}$$

Hence acceleration due to gravity is given by

$$g={2h \over t_1^2}$$