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## Homework Statement

An artillery shell is fired at mach 2 at an enemy encampment located at a range of 1700m. The initial position of the shell is 72 meters below the encampment, and is aimed at an angle

*θ*.

Solve the problem for

*θ*.

We can get the following variables/data from this:

Range = 1700m

Vertical displacement = 72m

Initial speed = 800m/s

## Homework Equations

From this I derived these equations:

1700=800cosθt (d = r*t)

72 = 800sinθt - 4.905t^2 (d = Vi*t + 1/2a*t^2)

2 equations with two unknowns. Problem is, I don't know how to solve them.

## The Attempt at a Solution

What I attempted was solving for t in the first equation, giving me t = (1700)/(800cosθ). Plugging this back into the second equation, I get 72 = 800sinθ(1700/800cosθ) - 4.905(1700/800cosθ)^2

From here, I got crazy solutions that ended up putting me at 89.5772 degrees for θ, which is incorrect. How can I correctly solve this?