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 Mar 13th 2017, 08:23 PM #1 Junior Member   Join Date: Mar 2017 Posts: 3 Vectors help I cannot figure this question out, please help. 5 stars to best answer. Q: A boat that can travel 2.5 m/s on still water is now on a river that flows due East at a velocity of 2.0 m/s. What is the velocity of this point with reference to a point on the shore when the bot is headed 45.0° W of N (135°)? Thanks. Please show work I think the answer is 1.8m/s 6.30° E of N or something around that. Problem is I have no clue how to get that answer and I've spent hours on it, I swear.
Mar 13th 2017, 08:42 PM   #2

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 Originally Posted by ItsMeWaffles I cannot figure this question out, please help. 5 stars to best answer. Q: A boat that can travel 2.5 m/s on still water is now on a river that flows due East at a velocity of 2.0 m/s. What is the velocity of this point with reference to a point on the shore when the bot is headed 45.0° W of N (135°)? Thanks. Please show work I think the answer is 1.8m/s 6.30° E of N or something around that. Problem is I have no clue how to get that answer and I've spent hours on it, I swear.
What have you tried? If we know that then we can help you better.

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Mar 13th 2017, 09:23 PM   #3
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 Originally Posted by ItsMeWaffles I think the answer is 1.8m/s 6.30° E of N or something around that.
You're close ... the resultant magnitude is fine, however, the direction is slightly off.

What method did you use to attain that solution?

 Mar 13th 2017, 10:11 PM #4 Junior Member   Join Date: Mar 2017 Posts: 3 That's the right answer but I'm supposed to figure out how to get there. After using a bunch of numbers I found that 2.5cos45 gets the right speed and tan-1(0.5/4.5) gets the right angle, but I don't understand how to get to that point.
 Mar 14th 2017, 06:26 AM #5 Senior Member     Join Date: Aug 2008 Posts: 113 The problem is just finding the sum of the boat vector and current vector. v = b + c Using the method of vector components, in the x-direction ... $v_x=2.5\cos(135)+2$ in the y-direction ... $v_y=2.5\sin(135)$ $|v|=\sqrt{v_x^2+v_y^2}$ $\theta=\arctan\left(\dfrac{v_y}{v_x}\right)$ As I stated earlier, the direction of 6.3 degrees E of N is incorrect. Note you could also solve this using the cosine law and sine law. HallsofIvy likes this.

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### whats the velocity of this boat with references to a point on the shore when the boat is headed 45

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