To get the time, we just substitute h = 592 to the equation:
h = 212t - 16t^2
592 = 212t - 16t^2
16t^2 - 212t + 592 = 0
4t^2 - 53t + 148 = 0
Factoring,
(t - 4)(4t - 37) = 0
t = 4 s
t = 37/4 s
Since it requires the time in which the rocket FIRST reaches a height of 592, we choose the smaller, which is t = 37/4 s.
Hope this helps :3
A model rocket is launched with an initial velocity of 212ft/sec. It's height h, in feet, after t seconds is given by the formula h=212t-16t^2. After how many seconds will the rocket first reach a height of 592ft?
2 answers
*lol I'm sorry the smaller time is t = 4s. OMG XD