water bottle rockets

Question

the height in feet h of a bottle rocket launched from a rooftop is given in the equation h=-16t^2+320t+32, where t is the time in seconds.

after the rocket is fired, how long will it take to return to the ground? solve by compleating the square. round to the nearest tenth of a second.

Answer 1

David,

 

For this problem we need to find the time when h = 0!

 

So you set h = 0 = -16t² + 320t + 32

 

If we divide through by 16 and multiply by -1 we get:

 

t² - 20t - 2 = 0

 

use the quadratic formula to solve:

 

t = (-b ± √(b² -4ac))/2a

 

After solving and rounding off you should get 2 solutions:

 

t = -0.1 s and t = 20.1 s

 

The 1st solution -0.1 s doesn't work because that would be a time before the bottle rocket was launched at t = 0.

So the second solution is the one we're looking for.

 

t = 20.1 s