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?

Question

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Respuesta :

belgrad belgrad · Answer 1 · 2021-02-17T03:34:53+01:00

Answer:

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

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

Step-by-step explanation:

Step(i):-

Given that the polynomial function

h(t) = -16 t² + 1600 ...(i)

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

[tex]\frac{dh}{dt} = -16(2t)+0[/tex]

Equating zero

[tex]\frac{dh}{dt} = 0[/tex]

⇒ -32t =0

⇒ t =0

The sunglasses hit the ground at t=0 seconds

Step(ii):-

Again differentiating with respective to 't', we get

[tex]\frac{d^{2} h}{dt^{2} } = -32(1) = -32 <0[/tex]

The maximum height at t=0

h(t) = -16 t² + 1600

h(t) = 1600feet