# What is the height of the cliff? (Use 32 ft/s2 for the acceleration due to gravity.)A stone was dropped off a cliff and hit the ground with a speed of 112 ft/s. What is the height of the cliff?...

What is the height of the cliff? (Use 32 ft/s2 for the acceleration due to gravity.)

A stone was dropped off a cliff and hit the ground with a speed of 112 ft/s. What is the height of the cliff? (Use 32 ft/s2 for the acceleration due to gravity.)

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Expert Answers

beckden | Certified Educator

If acceleration is constant, v(t) = at + v(0), since v(0) = 0 (the stone was dropped), so

`t = (v(t))/(g) = (-112 ft//sec)/(-32 ft//sec^2) = 3.5 sec `

`s(t) = 1/2g t^2 + v(0)t + s(0) = 1/2(-32 ft//sec^2)(3.5 sec)^2 + 0 + 0 = -196 ft.`

So the cliff is 196 ft tall.