Question

*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?

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Answer 1

Answer:

The velocity is 4.094ft/s

Step-by-step explanation:

Given

$s(t) = -3t^2+100t+3$

$s(t) = 131$

Required

Find the velocity at 131ft

First, calculate the time taken to reach 131 ft

$s(t) = -3t^2+100t+3$

This gives:

$131 = -3t^2 + 100t + 3$

Rewrite as:

$3t^2 - 100t - 3 + 131 = 0$

$3t^2 - 100t +128 = 0$

Expand

$3t^2 - 96t - 4t + 128 = 0$

Factorize

$3t(t - 32) -4(t -32) = 0$

Factor out t - 32

$(3t - 4)(t -32) = 0$

Split

$3t - 4 =0\ or\ t - 32 = 0$

Solve for t

$t = \frac{4}{3}\ or\ t =32$

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

The velocity is calculated as:

$v = \frac{s}{t}$

So, we have:

$v = \frac{131}{32}$

$v = 4.094$