Projectiles Watch

maggiehodgson
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Here is the question
Two particles A and B are launched together in the same vertical plane. A is 60m above B. A is launched at 14 mps horizontally and B at 28mps at 45 degrees to the horizontal. Show that the particles collide after travelling 40m horizontally.

I am struggling. The book gives an answer using some huge formula but how would I do it from suvat?

I have said let them collide x m from A but it could collide with B as it was on its way up or on its way down. I managed to get x = 45 and from that the time of 15 root 2 over 7 but that doesn’t work.

I currently can’t post a pictutre. Tsr not being able to yet. Any pointer wold be useful in the meantime.

Thanks
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Quirky Object
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Try writing the vertical displacement of A when they collide in terms of the vertical displacement of B, and use that to form some equations in t?
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dextrous63
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Not sure where the other replies to this thread have gone. But they don't collide. Something is wrong/missing in the question.
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DFranklin
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(Original post by dextrous63)
Not sure where the other replies to this thread have gone. But they don't collide. Something is wrong/missing in the question.
She's reposted it. Really annoying when people do that...
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dextrous63
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(Original post by DFranklin)
She's reposted it. Really annoying when people do that...
Yep. Just noticed it. She can repost it as often as she likes but it won't change the fact that they won't collide for exactly the same reason that if you throw a banana horizontally off the top of a cliff and someone simultaneously fires a rifle at the bottom, then the banana will remain unscathed unless the angle of elevation of that bullet is somewhat steep
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maggiehodgson
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(Original post by dextrous63)
Yep. Just noticed it. She can repost it as often as she likes but it won't change the fact that they won't collide for exactly the same reason that if you throw a banana horizontally off the top of a cliff and someone simultaneously fires a rifle at the bottom, then the banana will remain unscathed unless the angle of elevation of that bullet is somewhat steep
I'm sorry. The re-post was genuinely unintentional. I was working on an iPad and I thought I hadn't sent it at all.

Here is the question in the attachment
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ThatGuy107
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Using A, resolve horizontally using SUVAT to find the time when A has travelled 40 meters horizontally. You then need to resolve vertically (gravity!) to find the vertical displacement

Then you resolve B both horizontally and vertically (using the time from A) to prove the displacement vectors are the same

Hope this helps!
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dextrous63
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(Original post by ThatGuy107)
Using A, resolve horizontally using SUVAT to find the time when A has travelled 40 meters horizontally. You then need to resolve vertically (gravity!) to find the vertical displacement

Then you resolve B both horizontally and vertically (using the time from A) to prove the displacement vectors are the same

Hope this helps!
We all know that. Trouble is that it doesn't work in this situation as the question is ill conceived.

The question indicates that t=40/14 for A
Trouble is that for B, the horizontal distance travelled is thus 40 / 14 root 2

So, they do not meet
Last edited by dextrous63; 1 month ago
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dextrous63
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(Original post by maggiehodgson)
I'm sorry. The re-post was genuinely unintentional. I was working on an iPad and I thought I hadn't sent it at all.

Here is the question in the attachment
Thanks. What textook is it (in case I have it lying about), or please send a piccie of the solution in case we're missing something.
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maggiehodgson
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The book is Edexcel A Level mathematics Year 2 student book. I'll attach a photo of the answer. As I said is uses a massive formula not suvat.
(Original post by dextrous63)
Thanks. What textook is it (in case I have it lying about), or please send a piccie of the solution in case we're missing something.
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maggiehodgson
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Hi

I've just used Desmos to plot the trajectories and they do indeed collide at x= 40, y=20. This is the answer you would get from using that formula but I still can't do it using suvat.
(Original post by dextrous63)
Not sure where the other replies to this thread have gone. But they don't collide. Something is wrong/missing in the question.
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mqb2766
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Its a bit hard to read your images (answer and question), but I'm presuming they're using the (standard) equation of a projectile
y=xtanθ - gx^2/2u^2cos^2θ
l've not verified it, but I have little doubt they do both pass through that point. But I'd suspect that its at different times so they do not collide.

There is no time in the formula, its simply a quadratic in x. Using standard SUVAT will involve time (simple parametric equation) as you're integrating up acceleration, hence its doomed to failure to find a point of intersection as they don't pass through the same point at the same time, hence no collision.

When you upload an image, could you check its not too blurred etc. Also, it would have been helpful to know something about the fact that they were expecting you to use a previous queston (projectile motion) to solve the problem. Rather than just stating its uses a huge equation, can you try and be specific with the details. It makes it easier for people to directly help. Thanks.
Last edited by mqb2766; 1 month ago
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maggiehodgson
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Here is the question word for word from the text book: (apologies for blurred photos)

Two particles, A and B, are launched at the same time in the same vertical plane, with A 60 m vertically above B. Particle A is launched horizontally and particle B at 45 degrees above the horizontal. The particles are launched at speeds 14 m/s and 28 m/s respectively. Show that the particles collide after travelling 40 m horizontally.

It definitely uses the word collide.

The answer in the book uses the equation y= xtanT - (gx^2)(1 + tan^2 T)/(2U^2) where T is the angle of projection above the horizontal and U is the initial speed.

I've never seen this equation before and was trying to use suvat. If they collide then the length of time they are in the air must be the same and their vertical distances added together must equal 60. But it didn't work out and I can't figure out why. If you have any explanation for that I would be most please to hear of it.

Thanks.


(Original post by mqb2766)
Its a bit hard to read your images (answer and question), but I'm presuming they're using the (standard) equation of a projectile
y=xtanθ - gx2/2u2cos2θ
l've not verified it, but I have little doubt they do both pass through that point. But I'd suspect that its at different times so they do not collide.

There is no time in the formula, its simply a quadratic in x. Using standard SUVAT will involve time as you're integrating up acceleration, hence its doomed to failure to find a point of intersection as they don't pass through the same point at the same time, hence no collision.

When you upload an image, could you check its not too blurred etc. It makes it easier for people to help. Thanks.
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mqb2766
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I've tried to explain it already? They should both pass through that point, but at different times. You could use suvat to find the two (different) times and verify it yourself?

The question is wrong to use the word collide. There are sometimes mistakes in maths books, this seems to be one of those times.

(Original post by maggiehodgson)
Here is the question word for word from the text book: (apologies for blurred photos)

Two particles, A and B, are launched at the same time in the same vertical plane, with A 60 m vertically above B. Particle A is launched horizontally and particle B at 45 degrees above the horizontal. The particles are launched at speeds 14 m/s and 28 m/s respectively. Show that the particles collide after travelling 40 m horizontally.

It definitely uses the word collide.

The answer in the book uses the equation y= xtanT - (gx^2)(1 + tan^2 T)/(2U^2) where T is the angle of projection above the horizontal and U is the initial speed.

I've never seen this equation before and was trying to use suvat. If they collide then the length of time they are in the air must be the same and their vertical distances added together must equal 60. But it didn't work out and I can't figure out why. If you have any explanation for that I would be most please to hear of it.

Thanks.
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ThatGuy107
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(Original post by dextrous63)
We all know that. Trouble is that it doesn't work in this situation as the question is ill conceived.

The question indicates that t=40/14 for A
Trouble is that for B, the horizontal distance travelled is thus 40 / 14 root 2

So, they do not meet
I’m afraid you’re wrong and it does indeed work with suvat. See the attached image;Name:  F228602A-65DB-4E89-B060-FDD6DD28C92C.jpg.jpeg
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mqb2766
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The times for each particle are different. They are not in the same place at the same time. They do not collide.
(Original post by ThatGuy107)
I’m afraid you’re wrong and it does indeed work with suvat. See the attached image;Name:  F228602A-65DB-4E89-B060-FDD6DD28C92C.jpg.jpeg
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Size:  45.3 KB
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ThatGuy107
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(Original post by mqb2766)
The Times for each particle are different. They are not in the same place at the same time. They do not collide.
Yes the times for each particle are different, this is because they have different speeds of projection so they MUST be different. Think about it you can have 2 people running 100m, the one who runs faster gets to 100m first.
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mqb2766
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We agree about them passing through the same point and at different times. Do you agree about the fact that they don't collide?
(Original post by ThatGuy107)
Yes the times for each particle are different, this is because they have different speeds of projection so they MUST be different. Think about it you can have 2 people running 100m, the one who runs faster gets to 100m first.
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ThatGuy107
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(Original post by mqb2766)
We agree about them passing through the same point and at different times. Do you agree about the fact that they don't collide?
I agree that the question is poorly phrased and if you conduct the question properly they shouldn’t collide, but I believe this text book will be looking for the answer 40 20
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mqb2766
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I think that's a yes, they don't colljde. Being in the same point at the same time would be a critical bit of info in an exam for a question like this.
Generally two quadratic projectile parabola like these will intersect at a couple of points. However it's rare the particles would collide. The question/answer made the mistake of not involving time in the answer and not checking.

(Original post by ThatGuy107)
I agree that the question is poorly phrased and if you conduct the question properly they shouldn’t collide, but I believe this text book will be looking for the answer 40 20
Last edited by mqb2766; 1 month ago
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