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A gun is fired in a valley. The location is a distance from the summit of a mountain on a map by a length of 4 inches which is on a scale of 1 inch to 1 mile. The sound of the gun is heard 25 seconds after the flash of the shot is observed. Determine height of the mountain above the valley.
Speed of sound - 1090 feet per second.
Formula:
rate * time = distance distance / rate = time distance / time = rate
25 seconds / 3600 seconds in 1 hour = 0.69444 hours.
1090 * 0.649444 = 756.9396 = 757 feet = 0.14 miles.
Answer provided with problem is more. Where did I make the miscalculation(s) ?
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Rate, Time, Distance - Distance
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Re: Rate, Time, Distance - Distance
by Guest » Fri Nov 28, 2014 9:00 pm
As usual the information posted for questions on this forum is not very sensible.
And your solution has shown no thought or reasoning whatsoever.
On a map you measure horizontal distance.
The gun is fired in a valley (4 inches on a scale 1 inch to 1 mile) = 4 miles from a mountain summit horizontal distance.....what shape is the mountain..??
Where is the observer ??..... is he at the mountain summit..??
The speed of light is many times faster than the speed of sound so we assume the gun is fired at the instant the observer sees the flash.
If the observer is on the mountain summit and the sound travels at 1090 feet per second for 25 seconds then he is 25 x 1090 = 27250 feet away = 5.16 miles.
Then the height of mountain is sqroot(5.15^2 - 4^2) = 3.26 miles above the valley.
It is near enough a ...... 3 x 4 x 5 triangle.
And your solution has shown no thought or reasoning whatsoever.
On a map you measure horizontal distance.
The gun is fired in a valley (4 inches on a scale 1 inch to 1 mile) = 4 miles from a mountain summit horizontal distance.....what shape is the mountain..??
Where is the observer ??..... is he at the mountain summit..??
The speed of light is many times faster than the speed of sound so we assume the gun is fired at the instant the observer sees the flash.
If the observer is on the mountain summit and the sound travels at 1090 feet per second for 25 seconds then he is 25 x 1090 = 27250 feet away = 5.16 miles.
Then the height of mountain is sqroot(5.15^2 - 4^2) = 3.26 miles above the valley.
It is near enough a ...... 3 x 4 x 5 triangle.
- Guest
Re: Rate, Time, Distance - Distance
by Guest » Fri Nov 28, 2014 9:56 pm
I thought rate, time, distance formula was used.
Answer given: 3 miles.
what shape is the mountain..?? Unknown
Where is the observer ??..... is he at the mountain summit..?? The problem did not state - I am assuming he is at the summit.
"Then the height of mountain is sqroot(5.15^2 - 4^2) = 3.26 miles above the valley."
One question:
Why is the square root used ?
Answer given: 3 miles.
what shape is the mountain..?? Unknown
Where is the observer ??..... is he at the mountain summit..?? The problem did not state - I am assuming he is at the summit.
"Then the height of mountain is sqroot(5.15^2 - 4^2) = 3.26 miles above the valley."
One question:
Why is the square root used ?
- Guest
Re: Rate, Time, Distance - Distance
by Guest » Sat Nov 29, 2014 8:32 am
I thought rate, time, distance formula was used.
Answer.... Yes so it was rate is 1090 feet per second and time is 25 seconds
So distance is rate multiplied be time..... 1090 x 25 = 27 250 feet OR 5 miles approx
Answer given: 3 miles........So is my answer when rounded to nearest mile.
what shape is the mountain..?? Unknown...We don't need to know it.
Where is the observer ??..... is he at the mountain summit..?? The problem did not state - I am assuming he is at the summit............My calculations assumes he is at the summit listening for the gunshot coming from the valley below.
"Then the height of mountain is sqroot(5.15^2 - 4^2) = 3.26 miles above the valley."
One question:
Why is the square root used ?
Answer..
You can imagine it as a right angled triangle 4 miles horizontal, 3 miles vertical and sloping (hypotenuse) side 5 miles.
The square of the hypotenuse is equal to the sum of the squares on the other 2 sides.
OR for our problem the square of the hypotenuse minus the square on the horizontal equals the square of the vertical side.
(5^2 - 4^2) = 3^2
So need to take the square root to get the vertical height.
So..... sqroot(5^2 - 4^2) = Sqroot(3^2) = 3
Sqroot(25 - 16) = sqroot(9) = 3
..............................................
Answer.... Yes so it was rate is 1090 feet per second and time is 25 seconds
So distance is rate multiplied be time..... 1090 x 25 = 27 250 feet OR 5 miles approx
Answer given: 3 miles........So is my answer when rounded to nearest mile.
what shape is the mountain..?? Unknown...We don't need to know it.
Where is the observer ??..... is he at the mountain summit..?? The problem did not state - I am assuming he is at the summit............My calculations assumes he is at the summit listening for the gunshot coming from the valley below.
"Then the height of mountain is sqroot(5.15^2 - 4^2) = 3.26 miles above the valley."
One question:
Why is the square root used ?
Answer..
You can imagine it as a right angled triangle 4 miles horizontal, 3 miles vertical and sloping (hypotenuse) side 5 miles.
The square of the hypotenuse is equal to the sum of the squares on the other 2 sides.
OR for our problem the square of the hypotenuse minus the square on the horizontal equals the square of the vertical side.
(5^2 - 4^2) = 3^2
So need to take the square root to get the vertical height.
So..... sqroot(5^2 - 4^2) = Sqroot(3^2) = 3
Sqroot(25 - 16) = sqroot(9) = 3
..............................................
- Guest
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