Adding and Subtracting vectors; Finding change in velocity

AI Thread Summary
The discussion revolves around calculating the change in velocity of a cricket ball hit by a batsman. The batsman faces north while the ball travels at 30 m/s towards him and is hit at 50 m/s towards square leg, which is west. The initial calculation yielded a change in velocity of Δv=58 m/s N59°W, but the correct answer is W31°N. The confusion arises from the use of trigonometric functions to determine the angle, with participants debating the correct application of tangent. Ultimately, the distinction between the two directional answers is clarified, highlighting the importance of understanding vector direction in physics.
ShannonBanana
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Homework Statement



A batsman hits a cricket ball traveling towards him at 30m/s over square leg at 50m/s. If the cricketer is facing north and square leg is west of him, what is the change in velocity of the ball?

Homework Equations



Δv= Final velocity subtract initial velocity.

The Attempt at a Solution



I've attached a picture of my working, so you might be able to see where I've gone wrong. From this diagram, I got correct the final "speed" but not the direction. My answer was Δv=58m/s N59°W, but the answer given says the direction should be W31°N.
I got my answer through tan-1(50/30) or tan-1(opposite over adjacent). To get the answer given, you would have to (by my reckoning) use adjacent over opposite, which doesn't seem to be right. Do I have θ in the right place? And, if so, why?

Thanks for the help :)
 
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ShannonBanana said:
N59°W, but the answer given says the direction should be W31°N.
Aren't they the same?
 
... Are you serious?? Wow, I'm feeling kind of dumb now... Thank you though! :D
 

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