SUVAT, mechanics. Help Watch
And the hint
My working out:
I only found one (acute) angle which satisfies the equations where the horizontal displacement is 40.9 metres and the vertical displacement is 0 metres. But as the diagram shows there should be two… what have I done wrong?
Initial thoughts are that since the centre is 50m away, the nearest entry point is 49.95m away, and the furthest is 50.05m away (not sure where you get 40.9m, unless I'm being daft, which is entirely possible). In any case, these will produce 2 angles.
The difference in angles isn’t due to the fact that the horizontal distance travelled is different, it’s the same. Imagine the arc that the golf ball travels as theta goes from 0 to 90°. When it’s starting from 0 it won’t go far enough to reach the hole. Then it will reach it and go past it. As you start getting closer to 90° it will start landing closer again and at some angle it will land in the hole again.
That's my take on the question, but I see your point.
I beg to differ. Is the question not asking you to find the angle which will lead to the ball landing at exactly 49.95m away, which will mean it will get in by just missing the nearest part of the rim, and also find the angle so it lands at 50.05m, in which case it will hit the furthest part and bounce back in?
How else can there be two different angles involved?
It’s asking for the difference between the smallest and biggest angles where it lands straight in (it says it’s a point particle so you can ignore it bouncing if the edge). As the diagram shows the smallest is when it is fired close to the horizontal and only just reaches. And largest when it is fired near the vertical and just reaches. If it was fired to the far side of the hole then the angles wouldn’t be as extreme.