Write an equation for the height of the penny at the time after it was dropped.

Question

A penny was dropped from the window of a building, 64 feet above the ground. Write an equation for the height of the penny, h, at the time t seconds after it was dropped.

Answer 1

Assumptions:

 

Dropped from rest, negligible air resistance, h=0 at ground

 

This becomes a constant acceleration problem:

 

h(t) = h0 + v0*t +(1/2)*a*t^2

 

h0 = initial height = 64 ft

 

v0 = initial vertical speed = 0 if dropped from rest

 

a = -g = -32.2 ft/^2

 

Combining all the above,

 

h(t) = (64 - 16.1*t^2) ft, with t inseconds