Question

The position equation is s = -16t^2 + vot + so where s is height of the object in feet, vo is the initial velocity of the object, and so is the initial height of the object, and t is the time in seconds.
A cargo plane flying at 8000 ft. over level terrain drops a 500-pound supply package.
a)    How long will it take the package to strike the ground?
b)    The plane is flying at 600 miles per hour. How far will the package travel horizontally during its descent?

Answer 1

A.      For this case, let us set the variables:

s = 0 (final destination on the ground)

t = unknown

vo = 0

so = 8000 ft

Using the equation, we calculate for t:

0 = -16 t^2 + 0t + 8000

t = 22.36 s

B.      For this case:

s = unknown

t = 22.36 s

vo = 600 miles/hr = 880 ft/s

so = 0

Using the equation, we calculate for s:

s = -16*(22.36)^2 + 880*22.36 + 0

s = 11, 677.29 ft = 2.21 miles