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Old Mar 13th 2017, 08:23 PM   #1
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Question 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.
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Old Mar 13th 2017, 08:42 PM   #2
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Originally Posted by ItsMeWaffles View Post
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.
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Old Mar 13th 2017, 09:23 PM   #3
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Originally Posted by ItsMeWaffles View Post
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?
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Old Mar 13th 2017, 10:11 PM   #4
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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.
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Old Mar 14th 2017, 06:26 AM   #5
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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.
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