Question

While hovering near the top of Ribbon Falls in Yosemite National Park at 1600 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) = -16t^2 + 1600.
When will the sunglasses hit the ground?

Answer 1

a)The sunglasses hit the ground at t=0 seconds

b)The maximum height h(t) = 1600feet

Explanation:

Step(i):-

Given that the polynomial function

h(t) = -16 t² + 1600 ...(i)

Differentiating equation (i) with respective to 't' , we get

`(dh)/(dt) = -16(2t)+0`

Equating zero

`(dh)/(dt) = 0`

⇒ -32t =0

⇒ t =0

The sunglasses hit the ground at t=0 seconds

Step(ii):-

Again differentiating with respective to 't', we get

`(d^(2) h)/(dt^(2) ) = -32(1) = -32 <0`

The maximum height at t=0

h(t) = -16 t² + 1600

h(t) = 1600feet