Question

What is the speed of an object when dropped from height if its initial velocity is zero, its gravitational acceleration constant and air drag negligible?

Answer 1

When an object is dropped from a height with an initial velocity of zero and neglecting air drag, its speed can be determined using the equation for the final velocity of an object undergoing free fall:

$v=\sqrt{2gh}$

where:

• $v$ is the final velocity (speed) of the object
• $g$ is the gravitational acceleration (approximately 9.8 m/s² on Earth)
• $h$ is the height from which the object is dropped

Since the initial velocity is zero, the final velocity will be the speed at which the object hits the ground.

Let's assume the object is dropped from a height of $h$ meters. Plugging in the values:

$v=\sqrt{2\cdot 9.8\cdot h}$

Simplifying:

$v=\sqrt{19.6h}$

Therefore, the speed of an object dropped from a height $h$ with an initial velocity of zero and neglecting air drag is given by the square root of $19.6$ times the height $h$.