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A level maths mechanics / physics question vertical motion watch

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    I have a question that asks you to calculate the time it takes for a particle that's projected vertically to return to the same position. I was given the initial speed.

    As far as I can tell, there's three ways to go about answering this question:

    1) Setting the displacement equal to 0.
    2) Working out the time taken to reach the highest point by setting velocity equal to 0 and doubling the answer.
    3) Setting the final velocity equal to the negative of the initial velocity.

    The trouble is that each answer is roughly similarly but not exactly the same, and I can't figure out where this variation comes from. I'm certain it's not a rounding error. Any ideas?
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    (Original post by RuneFreeze)
    I have a question that asks you to calculate the time it takes for a particle that's projected vertically to return to the same position. I was given the initial speed.

    As far as I can tell, there's three ways to go about answering this question:

    1) Setting the displacement equal to 0.
    2) Working out the time taken to reach the highest point by setting velocity equal to 0 and doubling the answer.
    3) Setting the final velocity equal to the negative of the initial velocity.

    The trouble is that each answer is roughly similarly but not exactly the same, and I can't figure out where this variation comes from. I'm certain it's not a rounding error. Any ideas?

    I would assume that the ball takes longer going up and is quicker going down? So number 2 shouldn't work?

    Can you please post a pic of the question? Thanks!

    Personally I usually use S=0
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    (Original post by I hate exams!)
    I would assume that the ball takes longer going up and is quicker going down? So number 2 shouldn't work?

    Can you please post a pic of the question? Thanks!

    Personally I usually use S=0
    oh yes thats true thank you
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    (Original post by I hate exams!)
    I would assume that the ball takes longer going up and is quicker going down? So number 2 shouldn't work?

    Can you please post a pic of the question? Thanks!

    Personally I usually use S=0
    That would depend whether there's air resistance or any other force that isn't constant (in the case of air resistance, it acts downwards when the ball is going up and upwards when it is going down).

    I agree that S=0 is the best way, especially when dealing with more complicated questions involving extra forces.
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    (Original post by TheMindGarage)
    That would depend whether there's air resistance or any other force that isn't constant (in the case of air resistance, it acts downwards when the ball is going up and upwards when it is going down).

    I agree that S=0 is the best way, especially when dealing with more complicated questions involving extra forces.
    I know that s=0 is the best way, I was just trying to enhance my understanding by thinking of other ways and seeing if I get the same answer. I realise now that I made a numerical mistake and I actually got the exact same answer with all three methods. The previous poster was wrong about time being different in each direction I think; in a vacuum chamber with no air resistance it should be the same because they just have opposite acceleration with opposite velocity.
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    (Original post by RuneFreeze)
    I know that s=0 is the best way, I was just trying to enhance my understanding by thinking of other ways and seeing if I get the same answer. I realise now that I made a numerical mistake and I actually got the exact same answer with all three methods. The previous poster was wrong about time being different in each direction I think; in a vacuum chamber with no air resistance it should be the same because they just have opposite acceleration with opposite velocity.
    With no air resistance, you'd be right - time would be the same in each direction. But when you start to deal with asymmetrical forces like air resistance, the time would be different.
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    (Original post by TheMindGarage)
    With no air resistance, you'd be right - time would be the same in each direction. But when you start to deal with asymmetrical forces like air resistance, the time would be different.
    Ok thank you. Btw when would I ever need to start thinking about quantifying air resistance? This is just basic motion at the moment.
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    (Original post by RuneFreeze)
    Ok thank you. Btw when would I ever need to start thinking about quantifying air resistance? This is just basic motion at the moment.
    I don't know. A few questions in M2 (not involving projectiles but other things like sliding on slopes) do include air resistance but they usually model it as a constant force. If it's not mentioned, don't model it .
 
 
 
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