Question

Use the position equation
s = −16t^2 + v0t + s0
as the model for the problem.

A cargo plane flying at 6000 feet over level terrain drops a 700-pound supply package.

(a) How long will it take the package to strike the ground? (Round your answer to two decimal places.)
(b) The plane is flying at 600 miles per hour. How far will the package travel horizontally during its descent? (Round your answer to two decimal places.)

Answer 1

A. To solve for the time it takes for the package to strike the ground, all we have to do is to plug in the given values in to the position equation:

s = −16 t^2 + v0 t + s0

Where,

s = distance of the plane from the ground = - 6000 ft       (negative since the package moves from top to bottom)

t = time for it to strike the ground = unknown

v0 = 0 since the package starts from rest

s0 = 0 since we take the plane as the reference point

Substituting the given values:

- 6000 = -16 t^2 + 0 * t + 0

16 t^2 = 6000

t^2 = 375

t = 19.36 s

 

B. s = v * t

where v = 600 miles / hr = 0.17 miles / s

s = (0.17 miles / s) * 19.36 s

s = 3.23 miles = 17,054 ft