# Math

posted by .

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?

• Math -

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

• Math-correction -

*lol I'm sorry the smaller time is t = 4s. OMG XD

## Similar Questions

1. ### math

A model rocket is launched with an initial velocity of 250 ft/s. The height, h, in feet, of the rocket t seconds after the launch is given by h = −16t2 + 250t. How many seconds after launch will the rocket be 730 ft above the …
2. ### Intermediate Algebra

A model rocket is launched from a height of 50 feet. the formula: h=-16t^2+70t+50 describes the rocket's height,h,in feet t seconds after it was launched. how long will it take the rocket to reach the ground.
3. ### math

A model rocket is launched with an initial velocity of 160 ft/s. The height, h, in feet, of the rocket t seconds after the launch is given by h = −16t2 + 160t. How many seconds after launch will the rocket be 350 ft above the …

A model rocket is launched with an initial velocity of 128 ft/s from a height of 70 ft. The height of the rocket, in feet, t seconds after it has been launched is given by the function s(t)=−16t^2+128t+70. Determine the time …
5. ### Math

A model rocket is launched with an initial velocity of 164ft/sec. It's height h, in feet, after t seconds is given by the formula h=164t-16t^2. After how many seconds will the rocket first reach a height of 400ft?
6. ### intermediate algebra

A model rocket Is launched from a height of 50ft. The formula h=-16t^2+70t +50 describes the rocket's height,h,in feet seconds after it was launched. How long will it take the rocket to reach to reachthe ground?