h= 16t^2+80t+2016 Projectile Height. A rocket is fired upward from some initial distance above the ground. It's height in feet, h, above the ground, t seconds after it is fired, is given by.... what is the maximum height (in ft.)?

Question

h= 16t^2+80t+2016      Projectile Height. A rocket is fired upward from some initial distance above the ground. It's height in feet, h, above the ground, t seconds after it is fired, is given by....       what is the maximum height (in ft.)?

anonymous · Answer

how long does it take the rocket to reach the maximum height? (seconds)

anonymous · Answer

infinity. do you mean h= -16t^2+80t+2016

anonymous · Answer

and... when rocket hits the ground, how many seconds did it take since fired?

anonymous · Answer

yes! sorry good eye, i wish i was smart in math :S lol

anonymous · Answer

1 second. it hits the ground after 14 seconds. it  sounds weird but thats what i got on my calc and in my head.

anonymous · Answer

(assuming -16t^2) max is where slope = derivative = 0. derivative is -32t + 80. -32t + 80 = 0 t = 80/32 = 2.5 s at peak. plug in to the equation to find height (2116). find the roots of the equation (where h=0) to find when the rocket hit the ground (14s). the graph: http://bit.ly/kCgHz3

anonymous · Answer

wow, so the peak height was 2116 feet?

anonymous · Answer

yep. he is right. peak is at 2.5 sec and at 2116. made a slight miscalculation sry.

anonymous · Answer

is ok thanks for your help! how long when the rocket hit ground though?

anonymous · Answer

14 seconds

anonymous · Answer

thnks!