Water depth from sonar echo with 870 ms return time

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dlre
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Please help! trying to catch up with class! topic: the speed of sound

Homework Statement



Determine the depth of water if an echo using sonar returns in 870 ms and the speed of sound in water is 5300 km/h.

Homework Equations



distance= speed * time
depth=distance/2

The Attempt at a Solution


time= 870s
speed= 5300km/h

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i'm stuck at the part on converting ms to h. i think the

the answer i got is 0.64km

870ms= 0.00024167h
distance = 5300*0.00024167 = 1.28
depth= 1.28/2 = 0.64
 
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i really have no idea. i missed two months of physics and now struggling.

i think it took 870 ms to return.
 
All units must be in same system (SI).

length in meter
time in second
 
isn't it?

does it matter?

if we'redoing this by meter and second, then this is my attempt

d= 5300000m/s *0.87 s = 4,611,000m
depth= 4,611,000/2 = 2,305,500

--------
 
did you converted hour in sec?? it will be 5300*1000/3600 m/s
 
i give up. I'm going to bed!

good night! thanks for helping
 
Your answer of .64km looks good to me (and seems like a reasonable depth). So this question seems to be mainly about unit conversions.
Start with 870 ms . Now we know that ms means milliseconds, and that milli means 10^-3
So 870 ms = 870 x 10^-3 s = .87 s

Or another way to think about this is to multiply the 870ms with the correct ratios to cancel out the ms units so that you are left with seconds :

870 ms x [tex]\frac{1s}{1000ms}[/tex] = .87s
Here you are left with seconds; as you can see the milliseconds have canceled out.

You could continue to convert this into hours:

.87s x [tex]\frac{1 min}{60s}[/tex] x [tex]\frac{1 hr}{60 min}[/tex] = 2.416...x 10^-4 hr
Here we are left with hours since the units of seconds and minutes have been eliminated.

Now for the question:

[tex]\frac{5300 km}{1 hr}[/tex] x [tex]\frac{1000 m}{1 km}[/tex] x [tex]\frac{1 hr}{60 min}[/tex] x [tex]\frac{1 min}{60 s}[/tex] = [tex]\frac{1472.222 m}{1 s}[/tex]

[tex]\frac{1472.222 m}{1 s}[/tex] x .87s = 1280.83 m

1280.83 / 2 = 640.4 m or .64 km