# Find unknown angle of Projectile

1. Mar 2, 2015

### h.s

I don't need the solution solved for me, but I need help with the method to find the solution.
1. The problem statement, all variables and given/known data

A projectile is launched from an unknown angle and expected to hit a target at a lower altitude.
The values given are the initial velocity, and the distance of the target from the launcher.

2. Relevant equations

3. The attempt at a solution
I've tried solving for time, angle, or final velocity but they each need another unknown variable. Any insight would be helpful.

2. Mar 2, 2015

### PeroK

A trajectory can be described as a parabola of the form $y = ax^2 + bx + c$, where usually $c = 0$ and $a, b$ are functions of $v, \theta$.

If you derive this equation that would be a good start.

3. Mar 2, 2015

### h.s

i don't have θ. would a be the initial velocity or average velocity? because I can't solve for average velocity

4. Mar 2, 2015

### PeroK

The parabolic equation is a general equation that doesn't require you to know the numerical value of any parameter. Do you understand the concept of working with unknowns as parameters, such as $v, \theta, x \ \ and \ \ y$?

5. Mar 2, 2015

### h.s

I'm still at a loss. Suppose I apply this equation. The line would pass through two coordinates (0, 1.13) at launch, then at (4.382, 0) when it hits the ground. How would I solve for θ?

6. Mar 2, 2015

### PeroK

You'll have one equation with one unknown. Solving for $\theta$ should be relatively simple if you can do the maths to get there.

7. Mar 2, 2015

### h.s

... I'll have one equation with two unknowns; I still don't have a and b..

8. Mar 2, 2015

### PeroK

a and b will be functions of v (which you know) and $\theta$

I'll give you a start:

$x = vtcos \theta$

$y = ?$

Then, try to eliminate t. It's over to you to do some maths, I'm afraid!

9. Mar 2, 2015

### h.s

What does that mean?

10. Mar 2, 2015

### h.s

i know x=vtcosθ and y=vtsinθ-1/2gt^2, but my problem is that I don't know how to go further without knowing t, nor θ

11. Mar 2, 2015

### PeroK

$x=vtcos\theta \ \Rightarrow \ t = \frac{x}{vcos\theta}$