Question

Can someone please explain how to do this? I've watched every video possible for this topic and I'm doing something wrong still


A model rocket is launched with an initial upward velocity of
54/ms.The rocket's height h (in meters) after t seconds is given by the following h= 54t-5t^2. Find all values of t for which the rocket's height is 26 meters.
Round your answer(s) to the nearest hundredth.

Answer 1

You need to solve the quadratic equation 54t - 5t² = h   [h=26]

$54t-5t^2=26 \\ -5t^2+54t-26=0 \ \ \ \ \text{divide both sides by (-1)} \\ 5t^2-54t+26=0 \\ \\ t_{1,2}= \cfrac{54б \sqrt{(-54)^2-4*5*26} }{2*5} = \cfrac{54б \sqrt{2396} }{10}= \cfrac{54б 48.949 }{10} \\ \\ t_1= \cfrac{54- 48.949}{10}=0.50 \ seconds \ \ \text{[to the nearest hundredth]} \\ \\ t_2= \cfrac{54+ 48.949}{10}=10.29 \ seconds \ \ \text{[to the nearest hundredth]}$

You got twol values of t for which the rocket's height is 26 meters. 
t = 0.5 seconds means the rocket is flying up and after 0.5 seconds it is at a height  of 26 meters.
t = 10.29 seconds means the rocket on the way back down and after 10.29 seconds it is at a height of 26 meters.

Hope it helps.