# Which Step Does It Land On?

A projectile is launched from an initial position $$(x,y) = (-\SI{4}{\meter},\SI{0}{\meter})$$. The projectile's initial speed is $$12\text{ m/s}$$ and it is launched at a $$\SI{75}{\degree}$$ angle with respect to the $$x$$-axis. There is a staircase with 4 steps, as pictured above. The top step begins at $$(x,y) = (\SI{0}{\meter},\SI{4}{\meter})$$ meters and the bottom step ends at $$(x,y) = (\SI{4}{\meter},\SI{0}{\meter})$$. Each step is $$\SI{1}{\meter}$$ wide and $$\SI{1}{\meter}$$ deep. The projectile flies over part of the staircase and lands on one of the steps. What is the $$x$$ coordinate of the landing point in meters?

Details and Assumptions

• The gravitational acceleration is in the $$-y$$ direction, with a magnitude of $$\SI{9.8}{\meter\per\second\squared}$$.
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