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## Homework Statement

A batsman hits a cricket ball travelling 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 :)