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Problem:

A skiff leaves a dock and heads toward a house across the river. The house is at a bearing of $\mathrm{N}\,64^{\circ}\mathrm{E}$ from the dock. There is a $1$ mile per hour current blowing due east. Determine the speed and direction the skiff would have to maintain so that the skiff's actual speed is $4$ miles per hour and moving directly towards the house.

I know you can solve this with vectors and using trigonometry, but how would I do this?

1 Answers 1

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Hint:

Firstly, the question asks that the skiff must move directly towards the house and for this to happen the current would need to be flowing due west, as this would then make sense as the westbound current will offset the eastward component of the skiff such that it travels in a straight line. So confirmation is needed on whether the direction of the current is due east or due west.

Otherwise we have:

enter image description here

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    So for the direction, you would use law of sines. But what about the speed? – 2017-02-14
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    @JenkinsMa Yes, use the law of sines. The speed is already given in the question (4 miles per hour). – 2017-02-14
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    But there is a 1 mile current, so then the speed would be different, right? – 2017-02-14
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    @JenkinsMa The 1 mile current is already taken into account in my diagram. The speed will not be different as the question _requires_ that the overall speed of the skiff is 4 miles per hour. – 2017-02-14
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    im still confused... sorry.... but the speed will be different because the speed's actual speed is 4 miles after the current... but without the current, it would go faster, right? – 2017-02-14
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    @JenkinsMa It's okay, the thing that is confusing you is the part of the question that says "Determine the speed and direction the skiff would have to maintain". But then the at the end of the question the "actual speed" of the skiff is required to _be_ 4 miles per hour. The skiff cannot have 2 speeds associated with it, that would be impossible. I think the question is ambiguous or badly worded at most. – 2017-02-14