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

[yemmdizzle006]

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.

 

[yemmdizzle006]

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?

 

[yemmdizzle006]

solution

x = horizontal range

c = speed of sound

d = depth

g = gradient

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

Thank you!