Hello,

I'm sorry that this is a bit of a rambling question. I'm having difficulty understanding how to assign the signs in these problems. The rest of the math I can do and I'm finding it really frustrating that I'm not understanding the signs on the vectors. I can get to the solutions but I feel like I'm fudging it and I'd really appreciate it if someone would look over my work and clarify the sign thing for me. Thank you.

The first part of the question, which I can do is, 'A particle is projected from pointwith a speedOat an angle of $\displaystyle \alpha$ above the horizontal and moves freely under gravity. When the particle has moved a horizontal distanceu, it's height abovexisO.y

Show that:

$\displaystyle y = x\tan\alpha - \dfrac{gx^2}{2u^2\cos^2\alpha}$

I was able to do this and I looked it up and found it's an expression of the equation of trajectory. It's the second part of the question that I'm having difficulty with, which is:

'A girl throws a ball form pointat the top of a cliff. The pointAis 8 m above a horizontal beach. The ball is projected with a speed of $\displaystyle 7 ms^-1$ at an angle of elevation of 45 degrees. By modelling the ball as a particle moving freely under gravity, find the horizontal distance of the ball fromAwhen the ball is 1 m above the beach.A

I can solve this by substituting into the equation given in the first part if take the displacementto be -7 m, I also hadyas -7, but since this was squared, the sign makes no difference.u

Solving:

$\displaystyle -7 = x\tan(45) - \dfrac{9.8x^2}{(2)(-7)^2\cos^2(45)}$, gives the correct answer.

I also tried solving the same problem without using the equation from the first part but instead using the vertical motion to find the time and then the horizontal motion to find the distance.

Using $\displaystyle s = ut + \dfrac{1}{2}at^2$, for the vertical motion.

Taking, as positive, since it's down, I get the correct time if I takeg, (a), $\displaystyle 7\sin45$, as negative and the displacement, 7 m, as positive.u

Solving:

$\displaystyle 7 = -7\sin(45) + \dfrac{1}{2}(9.8)t^2$, gives the correct time.

One of the things that's confusing me is the displacement, in one equation it's negative in the other it's positive. The main thing is that it took me for ever to get the signs right to get the correct answer. I had the equations correct but without the right signs it was impossible to get the correct answer. My concern is that I'm not really understanding the signs on the vectors and I would really appreciate some help understanding how to assign the signs.

Thank you.