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The fireworks display occur at 550.331 ft
The generic equation for a hyperbola provided by: is the best method for solving the problem in this instance.
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We presume that the y-axis is where the hyperbola's longer axis lies.
In this instance, the sound traveled a total of 1100 meters, and the value of a can be calculated as follows:
2a = 1100
a = 550ft
Given that the two people are 3 miles apart, we can calculate the value of c in feet as follows:
1 mile = 5280 feet
∴ 3 miles = 15840 ft = c
And this is how we may determine what b is worth:
Our equation is thus given by:
And for this case we want to find the value of x when y = 3ft=15840ft and solving for x we get,
x = 550.331 ft.
The fireworks display occur at 550.331 ft.
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You can use the cosine rule for this - you might have to change some of the letters around for it to make sense though. Hope this helps!
