*In a scene from "The Martian" Matt Damon

shoots a flare straight up into the sky. The

height (in feet) of the flare after t seconds is

given by

s(t) = -3t? + 100t +3

What is the velocity of the flare when it is

moving toward the ground and its position is

equal to 131 feet?

(

Respuesta :

Answer:

The velocity is 4.094ft/s

Step-by-step explanation:

Given

[tex]s(t) = -3t^2+100t+3[/tex]

[tex]s(t) = 131[/tex]

Required

Find the velocity at 131ft

First, calculate the time taken to reach 131 ft

[tex]s(t) = -3t^2+100t+3[/tex]

This gives:

[tex]131 = -3t^2 + 100t + 3[/tex]

Rewrite as:

[tex]3t^2 - 100t - 3 + 131 = 0[/tex]

[tex]3t^2 - 100t +128 = 0[/tex]

Expand

[tex]3t^2 - 96t - 4t + 128 = 0[/tex]

Factorize

[tex]3t(t - 32) -4(t -32) = 0[/tex]

Factor out t - 32

[tex](3t - 4)(t -32) = 0[/tex]

Split

[tex]3t - 4 =0\ or\ t - 32 = 0[/tex]

Solve for t

[tex]t = \frac{4}{3}\ or\ t =32[/tex]

Since 32 > 4/3, then the flare is going up at 4/3s and coming down at 32s

The velocity is calculated as:

[tex]v = \frac{s}{t}[/tex]

So, we have:

[tex]v = \frac{131}{32}[/tex]

[tex]v = 4.094[/tex]

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