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

Robbie Glider

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 = (-b \± √(b^2 - 4ac))/(2a)`

Where

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

So:

`s = (22 \± √((-22)^2 - 4*3*31))/(2*3)`

`s = (22 \± √(112))/(6)`

`s = (22 \± 10.6)/(6)`

Split:

`s = (22 + 10.6)/(6)\ or\ s = (22 - 10.6)/(6)`

`s = (32.6)/(6)\ or\ s = (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