Question

An object is falling from a height of d and reaches a final velocity of vf. Calculate velocity when the object has fallen a distance d/2.

Answer 1

Answer:

The final velocity, $v_{f}$, is gd.

Explanation:

The condition here is a free falling object. Thus from the third equation of motion under free fall, we have;

$v_{f}$ = $v_{i}$ + 2gs

where $v_{f}$ is the final velocity of the object, $v_{i}$ is the initial velocity of the object, g is the gravitational force and s is the height.

Since the object falls from a height of d, then $v_{i}$ = 0 m/s, and s = d.

So that;

$v_{f}$ = 0 + 2gd

   = 2gd

$v_{f}$ = 2gd

When the distance is $\frac{d}{2}$, $v_{i}$ = 0 m/s.

Then;

$v_{f}$ = 2g$\frac{d}{2}$

$v_{f}$ = g x d

When the object falls through the height $\frac{d}{2}$, then the final velocity is gd.