Jump to content

User:Nsh/Flare-question

From Wikipedia, the free encyclopedia

Problem: To find a (quadratic) equation relating the height of a flare to the time from firing, given the following information:

Height is 120 when t = 4
Height is 192 when t = 16
Maximum height occurs at t = 12

Let us form the solution in completed-square form:

The maximum height will occur when the first derivative is zero, ie:

Now we have two equations with two unknows, which can be solved simultaneously.

(1)
(2)

(1) - (2) yields:

Putting the results back into the first equation:

This gives us the final equation as: