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

Answer:

t = 8.017 or 0.608 (nearest hundredth)

Step-by-step explanation:

$h = 138t-16t^2$

when h = 78:

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

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

Using quadratic formula:

$t=\dfrac{138 \pm\sqrt{(-138)^2-(4 \cdot 16 \cdot 78)} }{2 \cdot 16}$

$\implies t=\dfrac{138 \pm\sqrt{14052} }{32}$

$\implies t=8.017, t = 0.608$