Question

A rod AB of length 8 units, having mid-point at S, is in a vertical position as shown below. The end A is sliding vertically down, while end B is moving horizontally to your right till it reaches the point C, which is 8 units from the point B. Draw the locus of the mid-point S, using a minimum of 8 positions of AB.

Hint:

When a rigid rod moves with one end sliding vertically and the other horizontally, the midpoint traces a circular arc. Utilize geometric or trigonometric methods to accurately determine intermediate positions.

Answer 1

Step 1: Analyzing the motion of the rod.
- Point A moves vertically downward, while point B moves horizontally to the right.
- The rod remains rigid and maintains a fixed length of 8 units.

Step 2: Determining the locus of midpoint S.
- As both ends of the rod move simultaneously in perpendicular directions, the midpoint S follows a quarter-circle trajectory.

Step 3: Plotting at least 8 positions of the rod.
- Identify and mark 8 distinct positions of the rod as it moves.
- Determine the corresponding midpoints S for each position.
- Smoothly connect these midpoints to visualize the curved path traced by S.