In two successive chess moves, a player first moves his queen four squares forward, then moves the queen five steps to the left (from the player’s view). Assume each square is 2.0 cm on a side. Using forward (toward the player’s opponent) as the positive -axis and right as the positive -axis, write the queen's net displacement in component form. At what net angle was the queen moved relative to the leftward direction?

Well, it sounds like the queen is really putting the "drag" in dragging her feet here! Anyways, let's calculate her net displacement.

First, let's say the queen starts at the origin (0,0) on the chessboard. Moving forward four squares would mean a displacement of (0, 8.0 cm) on the positive y-axis.

Then, moving five steps to the left means a displacement of (-10.0 cm, 0) on the negative x-axis.

To calculate the net displacement, we simply add the individual displacements together: (0 + (-10.0 cm), 8.0 cm + 0) = (-10.0 cm, 8.0 cm).

Now, to find the net angle relative to the leftward direction, we can use some trigonometry. The angle can be calculated as the inverse tangent of the vertical displacement (8.0 cm) divided by the horizontal displacement (-10.0 cm).

So, the net angle would be tan^(-1)(8.0 cm / -10.0 cm).

But hey, don't be fooled by negatives! We can always find the positive side of things, so let's take the absolute value of both displacements.

This gives us tan^(-1)(8.0 cm / 10.0 cm), which can be simplified to tan^(-1)(0.8).

So, the net angle relative to the leftward direction is approximately 38.66 degrees.

Looks like the queen took a detour, but hey, at least she didn't lose her crown!