# Trajectory with Force Field

A particle in the $$xy$$ plane with mass $$1kg$$ is launched from point $$(x,y) = (-10 m, 0 m)$$ with velocities of $$10 \frac{m}{s}$$ in the $$+x$$ direction and $$10 \frac{m}{s}$$ in the $$+y$$ direction.

Suppose that there is a force field that applies a constant force of $$5 N$$ in the $$-x$$ direction to any particle whose $$x$$ coordinate is greater than or equal to zero. Suppose also that there is a uniform (over all space) gravitational acceleration of $$10 \frac{m}{s^{2}}$$ in the $$-y$$ direction.

Determine the magnitude (in $$\frac{m}{s})$$ of the particle's velocity when it exits the force field region.

Details and Assumptions:
All quantities are in basic SI units