Question

A stone is dropped off a cliff and hit the ground with a speed of 120 ft/s . a) what is the equation for acceleration a(t), velocity v(t), and displacement/ position s(t)? b) what is the height of the cliff ?

Answer 1

dropped off would indicate no initial velocity; so v(0) = 0

v(0) = -32(0) + C = 0 when C=0

v(t) = -32t
.................................

v(t) = 120 = -32t; when t = |-15/4|

this tells us it fell for 15/4 seconds before hitting the ground.

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s(t) = -16 (15/4)^2 + Hi = 0, when Hi = 225

the initial height of hte cliff is 225 ft

the eqs are:

s(t) = -16 t^2 + 225
v(t) = -32t
a(t) = -32