A particle of mass \(\displaystyle m \) is moving along the +\(\displaystyle x \)-axis with a constant speed \(\displaystyle v_0 \). At time \(\displaystyle t = 0 \) it enters a region in space between two parallel plates which are separated by a distance \(\displaystyle h \) and are contained in the \(\displaystyle x \)-\(\displaystyle z \) plane. The figure shows a side view of the plates, the +\(\displaystyle z \) axis is out of the screen. While the particle is between the plates, it is acted on by both gravity and by a time varying force that points upward (along the +\(\displaystyle y \)-direction) and has magnitude \(\displaystyle F = bt \), where \(\displaystyle b \) is a positive constant that is sufficiently large such that the particle hits the top plate without ever touching the bottom plate.

**(Part 1)** What are the units of the constant \(\displaystyle b \)? Enter m for meters, s for seconds and kg for kilograms. Make a sketch of what you think the trajectory of the particle is as it moves through the plates. Draw a coordinate system showing the position of the particle at time \(\displaystyle t \). Clearly indicate your origin, choice of axis, and draw in the coordinate functions for the position of the particle at time \(\displaystyle t \)?