solving word problems with quadratic formula with irrational roots

Question

A model rocket is launched with an initial upward velocity of 126/fts

. The rocket's height h

 (in feet) after t

 seconds is given by the following.

=h−126t16t2

Find all values of t

 for which the rocket's height is 50

 feet.Round your answer(s) to the nearest hundredth. 

Answer 1

if you meant

h(t) = -16t^2 + 126t

then

h=50 = -16t^2 +126t

16t^2 -126 =-50

use complete the square or the quadratic formula

t = .20 and 15.55 seconds when the height = 50 feet

it reaches max height at 126/32 = 63/16 = about 3.94 seconds

it is at ground level at t=0 seconds and about 7.86 seconds

it's at 50 feet a little more than 0 seconds and a little less than twice 7.86 = 15.52 seconds

that's a calculus check on the answer found with algebra