Question

The pilot of a helicopter plans to release a bucket of water on a forest fire. The height y in feet of the water t seconds after its release is modeled by y = -16t2 - 2t + 400. The horizontal distance x in feet between the water and its point of release is modeled by x = 91t. To the nearest foot, at what horizontal distance from the target should the pilot begin releasing the water? ____ ft Use a number only.

Answer 1

ok, so you need to know the time it takes for the water to hit the ground (y = 0)
0 = -16t^2-2t+400 = t^2 + t/8 - 25
= (t+1/16)^2 - 25 - 1/64
1601/64 = (t+1/16)^2
5.002 = t + 1/16 (t needs to be positive here, just common sense really)
t = 4.94 s
Now, we simply check the horizontal distance travelled by the water during 4.94s
x = 91t = 91 * 4.94 = 449.455 ft

Answer 2

thx