Row Boat Diagram
Some more related Rates and optimization homework help please?
Okay this one might be a bit difficult to understand without a diagram but i’ll try to explain it.
A man launches a boat from point A on the bank of a river (that is 4 km wide) to reach point B, which is 10 km downstream on the opposite bank ASAP (so B is ten km east of the point directly across from point A). He can row directly across to point C and then run 10 km to B, or he can row directly to some point (D) that is between B and C (so not directly across from A but closer than from A to B), and then run to B. He can row at 5 km/hr and he can run at 7 km/hr. Where should he land to reach B ASAP? (So should he go directly across from A to C, then run 10 km east to B, or should he row to point D and then run 10-x km to point B–with x being the distance between C and D?). And it can be assumed that the water speed is negligible.
This sounds like a calculus or pre-calc problem.
Simplfy the problem description, he will row to D. D is some point from B to C (including B and C).
x = distance from D to C (the distance he runs)
y = distance from A to D (the distance he rows)
t = time to reach C
y = sqrt(4^2 + (10-x)^2)
t = (x / 10) + (y / 7)
Now you can replace y in the last equation with the upper equation.
Next simplfy if you can, the take the first derivative and look for at the zeros.
Good luck
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October 18th, 2008 in
Uncategorized | tags: row boat diagram