A stone was dropped off a cliff and hit the ground with a speed of 104 ft/s. What is the height of the cliff?

Question

A stone was dropped off a cliff and hit the ground with a speed of 104 ft/s. What is the height of the cliff?

Take the acceleration due to gravity to be -32 ft/s^2

Answer 1

104^2=2*32*s
s=169 ft

Answer 2

If the stone is simply dropped, at time t, the velocity would be 32x t. So set 104 equal to this to get t

Now, the distance tranversed in time t is -16 t^2.
So substiute t from the velocity calc and find the distance.

Answer 3

v=at, x=1/2a*t^2, from the first equation, t=v/a, now substitute this back into the second equation, x=(a*(v^2/a^2))/2=v^2/2a

So the height is 104^2/64=169ft.

Answer 4

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Answer 5

v^2=u^2+2as
u=0
s=v^2/(2a)
=104^2/(2*32)
=169ft

Answer 6

v² = v0² + 2ax and since v0 (initial velocity) is zero
104²/(2*32) = 169 ft.

HTH

Doug