A model rocket is launched with an initial upward velocity of 47 m/s . The rocket's height h (in meters) after t seconds is given by the following.

Question

Find all values of t for which the rocket's height is 27 meters.

Round your answer(s) to the nearest hundredth.

Answer 1

h(t) = -4.8t^2 + 47t

if the initial height is zero

set h(t) = 27 meters = -4.8t^2 + 41 t and solve for t

4.8t^2 -41t -27 = 0

use the quadratic formula and solve for t

at^2 + bt + c =0 where a =4.8, b = -41 and c= -27

plug those values into

t = -b/2a + or - (1/2a)sqr(b^2 - 4ac)

Answer 2

h(t) = 47t - 4.9t² = 27. I solve this equation using TI-84 graph: t = 0.61 s and t = 8.98 s