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I need help with integration

  1. Nov 23, 2012 #1
    1. The problem statement, all variables and given/known data

    ball is thrown in angle α (balistically) from height H.
    Waht is the placement vector in any moment?

    2. Relevant equations



    3. The attempt at a solution

    Ok I know acceleration is:
    a(t) = (0,−g)

    it means the velocity is:
    v(t)=(v0 cosα , v0 sinα − gt)

    But the answer says the location vector is
    r(t) = v0 cosαt,H + v0sinαt-(0.5gt2)/2)

    shouldn't be:
    r(t) = -v0 sinαt,H + v0cosαt-(0.5gt2)/2) ?

    When I do it my way the other parts of the problem turns wrong since my rx got a minus ....then I get equation of the type x2=-t (for instance).

    And the answer should come with tanα since my cos and sin are different I get cot....I dun get why it comes wrong since even if I mistook the minus I know for sure cos=sin and sin=>cos I can;t integrate it leaving it as it was can it be there is a problem with the answer?
    They didn't say the angle was referring to speed but actually the curve the ball was thrown at... can I integrate without integrating the cos and sin?
     
  2. jcsd
  3. Nov 23, 2012 #2
    I think it is better to change the 'sinαt' into 'tsinα'. This makes it more clear that the angle on which the sin operates is a constant α and does not depend on time.

    Note that the integration is with respect to the time t and hence the sin and cos terms are to be considered constant terms and not to be integrated.
     
  4. Nov 23, 2012 #3

    PhanthomJay

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    Looks like in that last term you and the answer key divided by 2 once too often
    the angle alpha is the angle with the horizontal at which the ball is thrown initially. It (and it's sin or cos) is therefore a constant.
     
  5. Nov 23, 2012 #4
    Thank you very much I completely missed it @.@.

    Was running in circles XD

    Thanks.
     
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