Suppose an object is dropped from a height h0 above the grou

Suppose an object is dropped from a height h₀ above the ground. Then its height after t seconds is given by

h = 16t² + h₀,

where h is measured in feet. Use this information to solve the problem.

A ball is dropped from the top of a building 63 ft tall. (Round your answers to three decimal places.)

(a) How long will it take to fall half the distance to ground level?

t = 1 sec

(b) How long will it take to fall to ground level?

t = 2 sec

Solution

h = 16t^2 + h0 where h is measured in feet and height h0 above the ground

a) ho = 63 ft Replcing this value in ou equation:

h = -16t^2 + 63

How long will it take to fall half the distance to ground level?

h = 63/2 ft = 31.5 ft

31.5 = -16t^2 + 63

16t^2 = 31.5 ----> t = sqrt( 31.5/16) = 1.403 second = 1sec (rounded off )

b) How long will it take to fall to ground level ?

h=0 . Caluclate t:

0 = -16t^2 + 63

t = sqrt( 63/16) = 1.98 sec = 2 sec ( rounded off)