When you drop a pebble from height H,it reaches the ground with speed V assuming there is no air resistance.From what height should you drop it so it will reach the ground with twice speed?
A) $\sqrt { 2 }$ H
B)2H
C)4H
D)8H
E)16H

Question

Quizplus · Accepted Answer

The speed of the pebble when it hits the ground is given by:

V = sqrt(2gh)

where g is the acceleration due to gravity and h is the initial height of the pebble. We want to find the new initial height, h', such that the pebble will reach the ground with twice the speed, or 2V:

2V = sqrt(2gh')

Solving for h', we get:

h' = 8h

Therefore, the pebble must be dropped from a height that is 8 times the original height in order to reach the ground with twice the speed. The only answer choice that matches this is C) 4H, since 4H x 8 = 32H, which is the new height of the pebble.

When You Drop a Pebble from Height H,it Reaches the Ground