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?
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 :)