# 2-D Motion Conceptual Problem

1. Oct 13, 2010

### k-rod AP 2010

1. The problem statement, all variables and given/known data
A ball is thrown horizontally from the top of a cliff with an initial Vo(at t=os). At any moment , its direction of motion makes an angle θ to the horizontal.

1)Derive a formula for θ as a function of time, t, as the ball follows a projectile's path.

2. Relevant equations

3. The attempt at a solution
components: Vx=Voxcosθ Vy=Voysinθ

then i plugged the x component to find t:Vx=x/t.... t=x/(Voxcosθ)

next i plugged t into a y position function Y=Yo+Voyt+1/2at^2

0=h+(Voysinθ )(x/Voxcosθ)+(1/2*-9.8*(x/Voxcosθ)^2)

this be correct because if u were given all of the initial heights and velocities the only variable left to solve for would be θ, giving you your answer right?

2. Oct 13, 2010

### PhanthomJay

That's a pretty long equation. The horizontal velocity is always constant: v_x = v_ox.
The vertical velocity is just v_y = gt.
You can solve for theta as a function of t using basic trig properties of a right triangle.

3. Oct 14, 2010

### k-rod AP 2010

hey thanks, but u can only solve for theta using trig for a 1-d motion problem, but in 2-d the object follows a parabolic path so its velocity must be broken into components.

the t=x/v_o cos(theta) gives you time which you plug in to the y position function, which accounts for the parabolic path.

if anybody else knows what to do, any help would be aprreciated

4. Nov 21, 2010

### k-rod AP 2010

Does anybody else know how to solve this, I am really curious what the correct procedure is....

5. Nov 21, 2010

### Condensate

If it helps you, I would start by sketching out a graph showing the function of time (Y) and its relationship to t. You can completely ignore X since it will have nothing to do with how quickly Y changes. Y is only a function of time.

From there on out, follow PhanthomJay's suggestions.

6. Nov 22, 2010