Find Range of Ray Emitted Horizontally at Depth 150m in Water

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SUMMARY

The problem involves calculating the horizontal range of a sound ray emitted from a depth of 150 meters in water, where the speed of sound is 1600 m/s at the surface and increases linearly at a rate of 0.017 m/s². The correct formula to determine the horizontal range (x) is derived from the curvature of the ray, given by x = sqrt((2 * c * d) / g). Using this formula, the correct horizontal range is found to be 4200 meters, contrasting with an incorrect initial calculation of 883880 meters.

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Homework Statement


speed of sound in water is 1600m/s at the surface and increases linearly with depth at a rate of 0.017/s, find the range at which a ray emitted horizontally at a source of dept 150m will reach the surface


C = sound speed in water (1500m/s)

gradient = g (0.017/s)

Homework Equations



Relevant equations I used will be calculate the Radius of the curvature of the Ray

R (curvature of Ray) = c0/g


The Attempt at a Solution



I keep getting a huge figure 883880m ...

and i know it is not correct.
 
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apparently the answer is that at 4200m, the ray emitted horizontally will reach the surface.I have no idea how my teacher came up with that.Is there some piece of information I am missing?
 
solution

x = horizontal range

c = speed of sound

d = depth

g = gradient

x = sqrt( (2*c*d) / g))

Thank you!
 

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