Quadratic Word Problem

Question

A model rocket is launched with an initial upward velocity of 188/fts

. The rocket's height h

 (in feet) after t

 seconds is given by the following.

h=188t-16t^2

Find all values of t for which the rocket's height is 92 feet

Answer 1

92 = 188t - 16t^2.

Rewrite the equation as 16t^2 - 188t + 92 = 0

Use the quadratic formula to find t.

t = [-b +/- sqrt(b^2 - 4ac)] / 2a, where a=16, b=-188 and c=92.

t = [-(-188) +/- sqrt((-188)^2 - 4*16*92)] / 2*16 = [188 +/- sqrt(35,344 - 5888)] / 32 = [188 +/- 171.6275] / 32 = 0.5116 and 11.2384. The first time is during the rocket's ascent and the second time is during descent.