# I need help with integration

1. Nov 23, 2012

### Lenjaku

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. Nov 23, 2012

### grzz

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.

3. Nov 23, 2012

### PhanthomJay

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.

4. Nov 23, 2012

### Lenjaku

Thank you very much I completely missed it @.@.

Was running in circles XD

Thanks.