Question

Melissa and Robbie are flying remote control gliders. The altitude of Melissa’s glider, , in feet, is modeled by this function, where s is time, in seconds, after launch. The altitude of Robbie’s glider is modeled by function r, where s is time, in seconds, after launch.

Answer 1

Answer:

Robbie Glider

Step-by-step explanation:

Given

Melissa Glider

$m(s) = 0.4(s^3 - 11s^2 + 31s - 1)$

Robbie Glider

See attachment for function

Required

Which reaches the greater maximum within the first 6 seconds

Melissa Glider

First, we calculate the maximum of Melissa's glider

$m(s) = 0.4(s^3 - 11s^2 + 31s - 1)$

Differentiate:

$m'(s) = 0.4(3s^2 - 22s + 31)$

Equate to 0 to find the maximum

$0.4(3s^2 - 22s + 31) = 0$

Divide through by 0.4

$3s^2 - 22s + 31 = 0$

Solve for s using quadratic formula:

$s = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

Where

$a = 3; b = -22; c = 31$

So:

$s = \frac{22 \± \sqrt{(-22)^2 - 4*3*31}}{2*3}$

$s = \frac{22 \± \sqrt{112}}{6}$

$s = \frac{22 \± 10.6}{6}$

Split:

$s = \frac{22 + 10.6}{6}\ or\ s = \frac{22 - 10.6}{6}$

$s = \frac{32.6}{6}\ or\ s = \frac{11.4}{6}$

$s = 5.4\ or\ s = 1.9$

This implies that Melissa's glider reaches the maximum at 5.4 seconds or 1.9 seconds.

Both time are less than 6 seconds

Substitute 5.4 and 1.9 for s in $m(s) = 0.4(s^3 - 11s^2 + 31s - 1)$ to get the maximum

$m(5.4) = 0.4(5.4^3 - 11*5.4^2 + 31*5.4 - 1)$

$m(5.4) = 1.24ft$

$m(5.4) = 0.4(1.9^3 - 11*1.9^2 + 31*1.9- 1)$

$m(5.4) = 10.02ft$

The maximum is 10.02ft for Melissa's glider

Robbie Glider

From the attached graph, within an interval less than 6 seconds, the maximum altitude is at 3 seconds

$r(3) = 22ft$

Compare both maximum altitudes, 22ft > 10.02ft. This implies that Robbie reached a greater altitude