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word problem!! HELP!! HELP!!?
If a toy rocket is fired upward into the air from the top of a 10-foot ladder with a velocity of 72 ft/s, its height above the earth (in feet) after t seconds is given by f(t)= -16t^2 + 72t + 10.
after how many seconds does the toy rocket hit the ground? Round to the nearest hundreth of a second.
(the answer is app. 4.63 seconds, but im not getting that answer! please help!?) i dont know if this will help, but i had to figure out the height of the rocket after 1 second, which is=66 feet. the rocket reaches its maximum height at 2.25 seconds. and the maximum height reached by the rocket is 91 feet.
f(t)= -16t^2 + 72t + 10
You need to find when f(t) = 0
So
-16t^2 + 72t + 10 = 0
t^2 - 9t/2 - 5/8 = 0
(t - 9/4)^2 - 81/16 - 5/8 = 0
(t - 9/4)^2 = 91/16
t = 9/4 + [sqrt(91)]/4 or 9/4 - [sqrt(91)]/4 but time is positive so take
t = 9/4 + [sqrt(91)]/4
= 18.54/4 = 4.63 seconds
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