Which Step Does It Land On?

A projectile is launched from an initial position (x,y)=(4 m,0 m)(x,y) = (-\SI{4}{\meter},\SI{0}{\meter}). The projectile's initial speed is 12 m/s12\text{ m/s} and it is launched at a 75 °\SI{75}{\degree} angle with respect to the xx-axis. There is a staircase with 4 steps, as pictured above. The top step begins at (x,y)=(0 m,4 m)(x,y) = (\SI{0}{\meter},\SI{4}{\meter}) meters and the bottom step ends at (x,y)=(4 m,0 m)(x,y) = (\SI{4}{\meter},\SI{0}{\meter}). Each step is 1 m\SI{1}{\meter} wide and 1 m\SI{1}{\meter} deep. The projectile flies over part of the staircase and lands on one of the steps. What is the xx coordinate of the landing point in meters?

Details and Assumptions

  • The gravitational acceleration is in the y-y direction, with a magnitude of 9.8 ms2\SI{9.8}{\meter\per\second\squared}.
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