Half speed

Classical Mechanics Level 2

Ian and the Doctor drop a stone off a 180 meter high cliff. How many meters above the ground will the stone be when its speed is exactly half its impact speed? As the TARDIS has negated all air resistance within the region, it may be safely neglected. (Use 10 meters per second squared for the surface gravity value.)


The answer is 135.

Edward Gleason by Edward Gleason , 51, USA

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2 solutions

Edward Gleason
Dec 20, 2015

First, calculate the time required for the stone to reach the ground:

x = (0.5)g(t)^2
180 = 0.5g(t)^2
180 = 0.5(10)(t)^2
180/5 = 36 (36)^1/2 = 6


The stone reaches the ground in six seconds: Its speed: v = (10)(6) = 60 m/s

We need to find the position at which the stone's descending speed is 30 m/s

v = gt 30 = (10)t t = 3 s

At three seconds:
x = (0.5)(10)(3)^2
x = 5(9) = 45 meters

The stone has fallen 45 meters when its descending speed is 30 m/s, or half its impact speed. At this position, the stone is 135 meters above the ground.

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Nahid Tuli
Dec 21, 2015

Here at first case, we have velocity=v, gravity=g=10ms^-2 and displacement =s=180 Suppose, the matter is x meter above the ground.

Firstly, we know V^2=u^2+2as

v^2=u^2+2 10 s

v^2=0+20s

v^2=20s....1no .equation and

1/4v^2=u^2+2a(s-x)....2no equation

now divide 2 no eq by 1 no equation You will get the value of x

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