# Trajectory with Force Field

**Classical Mechanics**Level 3

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

Give your answer to three decimal places