# hyperbola/lightning strike

• Nov 25th 2007, 12:05 PM
tle8807
hyperbola/lightning strike
Two people, standing 1 mile apart, both see a flash of lightning. After a period of time, a person at point 'A' hears thunder. 2 seconds pass, and then person at point 'B' hears thunder. Assume that person at point 'B' is due West of person at point 'A' and the lightning strike is known to have occured due North of person at point 'A'. Where did the lightning strike? Graph the solution.

Sound travels at 1100 ft. per second
1 mile is 5280 ft.

• Nov 25th 2007, 01:26 PM
Soroban
Hello, tle8807!

You don't need hyperbolas for this . . . just Pythagorus.

Quote:

Two people, standing 1 mile apart, both see a flash of lightning.
After a period of time, a person at point 'A' hears thunder.
Two seconds pass, and then person at point 'B' hears thunder.
Assume that person at point 'B' is due West of person at point 'A'
and the lightning strike is known to have occured due North of person at point 'A'.
Where did the lightning strike? Graph the solution.

Sound travels at 1100 ft. per second
1 mile is 5280 ft.

Code:

                        L                         *                       / |                     /  |                   /    |         x+2200  /      |               /        | x             /          |           /            |         /              |       * - - - - - - - - *       B      5280      A

$AB = 5280$ feet.
The lightning strikes at $L.$
Let $x = AB$

Point $B$ is 2200 feet further from $L$: . $BL \:=\:x+2200$

Pythagorus says: . $x^2 + 5280^2 \:=\:(x+2200)^2$

. . and we have: . $4400x \:=\:23,038,400\quad\Rightarrow\quad x \:=\:5236$ feet.

• Nov 26th 2007, 05:46 AM
tle8807
Thanks
I ended up figuring it out last night. Thanks anyways.