Originally posted by: Eeezee
Originally posted by: 91TTZ
Originally posted by: Dritnul
Originally posted by: 91TTZ
Originally posted by: Mark R
Treat the home, stadium and storm as the three points of a triangle. You know the lengths (either given in the question, or from the time delay).
Then use cosine rule to find the angle. Due to symmetry there are 2 solutions.
That seems to imply that the storm cloud is at ground level, which it's not. You need to take altitude into account.
So now that there's altitude to deal with, there are many more than 2 solutions. You wouldn't have just left/right to contend with, you'd have a points in between at various altitudes.
however no altitude is given so its kinda hard to assume an altitude w/o at least a cloud type
besides its only university physics so its still slightly simplified physics
But if they're trying to find an answer to this problem, how can they ignore very basic factors which affect the result? They want an answer but are assuming that a cloud has no altitude? Why even give an answer if it's most likely wrong?
Because technically there are an infinite number of xyz coordinates for the cloud. The answer specifically asks for "where does the lightning strike?" The cloud doesn't generate the sound. You're hearing ionized air, so the noise comes from all along the lightning strike. Due to the speed of sound being approximately constant and due to obvious geometric reasons, you'll hear the lightning as it strikes the ground before you'll hear the lightning coming from the cloud.
In other words, all of the information assumes you hear the thunder originating from the ground. This only makes sense, the beginning of the thunder (the beginning of the rumbling) corresponds to the point on the ground where the lightning bolt struck.
But since you're trying to find out where the sound is coming from in relation to the house and the stadium, you can't really tell from the info provided. I'm sure they're looking for an answer along the lines of "if you hear the zap over the radio at 4:00:00, the thunder takes 2 second to get to the stadium and 4 seconds after that to get to the house, then the cloud is here at x,y" I'm sure they want that, but you can't really figure that out.
For one, not all lightning reaches the ground. In fact, most doesn't. That cloud could be 2 miles up. You can't really tell how far between the house and the stadium (ground wise) the cloud is, since we're not dealing with a 2 dimensional space.
For instance, sound travels at 340 meters/second on an average day. Let's say the house is 680 meters due south of the stadium. Let's say the sound reaches the stadium and the house at the same time, 2 seconds. You'd figure that the cloud has to be 680 meters from both the house and the stadium, meaning it's off to the left or right side of both the stadium and house.
But in reality, that doesn't have to be the case. The cloud could be directly in between. You might think that since it's in between, and the house and stadium are only 680 meters apart, that the sound would only take 1 second to get to each. But that's where altitude comes into play. The thunder could still be originating 680 meters from both the house and the stadium, it's just up in the air.
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