Question

while hovering near the top of a waterfall in a national park at 6400 feet, a helicopter pilot accidentally drops his sunglasses. the height h(t) of the sunglasses after t seconds is given by the polynomial function h(t)= - 16t² + 6400. when will the sunglasses hit the ground? the sunglasses will hit the ground after seconds.

Explanation:

Step1: Set height to 0

When the sunglasses hit the ground, $h(t)=0$. So we set $-16t^{2}+6400 = 0$.

Step2: Solve for $t^{2}$

First, move the terms around: $16t^{2}=6400$. Then divide both sides by 16: $t^{2}=\frac{6400}{16}=400$.

Step3: Solve for $t$

Take the square - root of both sides. Since $t$ represents time and cannot be negative in this context, $t=\sqrt{400}=20$.

Answer:

20