Question

The minute hand of a wall clock measures 16 cm from its tip to the axis about which it rotates. The magnitude and angle of the displacement vector of the tip are to be determined for three time intervals. What are the (a) magnitude and (b) angle from a quarter after the hour to half past, the (c) magnitude and (d) angle for the next half hour, and the (e) magnitude and (f) angle for the hour after that? Give all angles as positive values measured counterclockwise from the +x direction (to the right, or 3 o'clock).

Answer 1

The magnitude and angle of the displacement vector of the wall clock's minute hand for different time intervals can be determined using trigonometry.

Step-by-step explanation:

To determine the magnitude and angle of the displacement vector of the wall clock's minute hand for different time intervals, we can use trigonometry.

(a) For the time interval from a quarter after the hour to half past, the magnitude of the displacement vector is 8 cm (half the length of the minute hand), and the angle can be calculated as 45 degrees counterclockwise from the +x direction.

(b) For the next half hour, the magnitude remains the same at 8 cm, and the angle increases by 30 degrees to a total of 75 degrees counterclockwise.

(e) For the hour after that, the magnitude remains the same at 8 cm, and the angle increases by another 30 degrees to a total of 105 degrees counterclockwise.