What Am I Doing Wrong with My Vector Velocity Calculations?

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The user is struggling with vector velocity calculations for an upcoming test, specifically regarding the motion of a boat across a stream. They initially calculated the boat's speed as 4.27 m/s, assuming it was directed straight across, which does not account for the current's effect. To move directly across, the boat needs to be angled upstream to counteract the current, resulting in a lower effective speed. The discussion emphasizes the importance of vector components in determining the correct velocity. Clarification on these calculations is sought to improve understanding before the test.
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I really need help as I have a test tomorrow and am having trouble with these problems.

I have attached the questions and my work in the picture below.

http://img79.imageshack.us/img79/9886/scan0001po5.th.gif

Both answers are wrong. Can somebody tell me what I am doing wrong and if my diagrams are drawn correctly. Any help would be appreciated. Thank you.
 
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Hi xCanx,

xCanx said:
I really need help as I have a test tomorrow and am having trouble with these problems.

I have attached the questions and my work in the picture below.

http://img79.imageshack.us/img79/9886/scan0001po5.th.gif

Both answers are wrong. Can somebody tell me what I am doing wrong and if my diagrams are drawn correctly. Any help would be appreciated. Thank you.

The speed you found for the boat (4.27 m/s) would be the speed if the boat was pointed directly across the stream. In that case, the current would drag the boat downstream, so it does not match the problem.

In this case, they want the boat to actually move straight across the water. So the boat must be pointed somewhat upstream, so as to cancel out the effect of the water. Since some of its velocity is being used to cancel the water, the total velocity should be less than 4m/s.

Does this help? What do you get?
 
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