# SUVAT, mechanics. HelpWatch

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#1
I’m answering a question on Isaac physics and I can’t figure out what I’m doing wrong:

Question here:

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?
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1 week ago
#2
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.
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#3
(Original post by dextrous63)
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.
Oh yeah whoops radius is 0.05m. not sure how i got 40.9 either. Surely that shouldn’t change the amount of solutions though ? I’ll try it now though
Last edited by Maximus 190; 1 week ago
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#4
Oh I figured out why. I didn’t say 30* sintheta for the vertical velocity
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1 week ago
#5
(Original post by Maximus 190)
Oh yeah whoops radius is 0.05m. not sure how i got 40.9 either. Surely that shouldn’t change the amount of solutions though ? I’ll try it now though
Yes it does. The ball can either just miss the near part of the rim or hit the furthest part. These are 2 different distances, so will produce 2 different angles,
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#6
(Original post by dextrous63)
Yes it does. The ball can either just miss the near part of the rim or hit the furthest part. These are 2 different distances, so will produce 2 different 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.
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1 week ago
#7
(Original post by Maximus 190)
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.
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?

That's my take on the question, but I see your point.
Last edited by dextrous63; 1 week ago
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#8
(Original post by dextrous63)
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.
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#9
How do I solve this though? Is there an identity I should know or something?
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1 week ago
#10
(Original post by Maximus 190)
How do I solve this though? Is there an identity I should know or something?
Double angle formula. Year 13 skill.
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1 week ago
#11
As you've not done it yet, you'll eventually find out that

sin2x =2sinxcosx
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#12
(Original post by dextrous63)
Double angle formula. Year 13 skill.
Oh right nice, thanks
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1 week ago
#13
(Original post by Maximus 190)
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.
It's interesting how there's more than one way to interpret the same problem.
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