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

Question

The height in feet h of a water bottle rocket launched from a rooftop is
given by the equation h = -16 t
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?

Answer 1

 h = -16t^2 + 320t + 32

 

Ground is h =0.

 

   - 16 t^2 + 320 t + 32 = 0.

 

     - t^2 + 20 t + 2 =0

 

      t = -20/2 ±(√(400 + 8)

                          2

 

         t = -10 + √408 = 10.2 sec  / negative answer is not acceptable.

Answer 2

Hey Noah -- physically, we're launching vs. gravity at 320 ft/s at t=0 from height 32ft ...

 

gravity negates the speed by 32ft/s each second ... flight takes 10s to peak ...

 

another 10s is needed to return to rooftop level ... the last 32ft to ground takes only 

 

another 0.1s since we're diving 320ft/s ==> total time ~ 20.1 sec  ... Regards :)