Question

A model rocket is launched with an initial upward velocity of 138 ft/s. The rocket's height h (in feet) after 1 seconds is given by the following.

h = 138t-16t^2
Find all values of 1 for which the rocket's height is 78 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)

Answer 1

t = 8.017 or 0.608 (nearest hundredth)

Explanation:

`h = 138t-16t^2`

when h = 78:

`\implies 138t-16t^2=78`

`\implies 16t^2-138t+78=0`

Using quadratic formula:

`t=(138 \pm√((-138)^2-(4 \cdot 16 \cdot 78)) )/(2 \cdot 16)`

`\implies t=(138 \pm√(14052) )/(32)`

`\implies t=8.017, t = 0.608`