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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