hyperbola/lightning strike

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November 25th 2007, 11:05 AM
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.

Please help me.
November 25th 2007, 12:26 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.
November 26th 2007, 04:46 AM
tle8807

Thanks

I ended up figuring it out last night. Thanks anyways.