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## Homework Statement

It's a projectile problem.

Basically, you launch a projectile starting from a height ΔY (0.5 m) at speed V0 at an angle θ. Then after time T, the projectile then hits the ground (0m) and sticks to the ground, traveling distance ΔX.

The question goes if you are given ΔX and V_0 (which are known variables, but there is no numerical number to go with it), solve for θ.

Essentially, solve for θ given Delta X, Delta Y, and V0

## Homework Equations

[itex]Acceleration (A) = -9.81 m/s^2 [/itex]

[itex] ΔY = -0.5 m [/itex]

[itex] Vx = V_0 Cos θ [/itex]

[itex] Vy = V_0 Sin θ [/itex]

[itex] ΔY = V_0 Sin θ T + \frac{AT^2}{2}[/itex]

[itex] ΔX = V_0 Cos θ T [/itex]

## The Attempt at a Solution

I tried solving for T in terms of ΔX, V0, and θ by using the 6th equation.

[itex] T = \frac{ΔX}{V_0 Cos θ} [/itex]

Then attempted to plug this value of T into the 5th equation.

[itex] ΔY = \frac{V_0ΔX Sinθ}{V_0Cosθ} + \frac{A}{2}\frac{ΔX^2}{V_0^2 Cos^2}[/itex]

Simplified

[itex] ΔY = \frac{ΔX Sin θ}{Cos θ} + \frac{AΔX^2}{2V_0^2 Cos^2 θ} [/itex]

Then I multiplied both sides by [itex]Cos^2 θ[/itex].

[itex] (ΔY Cos^2 θ) = (Sinθ Cos θ ΔX) + \frac{AΔX^2}{2V_0^2} [/itex]

And now I'm stuck and I'm not sure what I should do. I don't know if my original approach will get me to my desired answer.

If any clarification is needed, I will gladly provide some.

Thank you, any help would be greatly appreciated.

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