Final answer:
The minute hand rotates counterclockwise with an angular velocity of 0.1 radian per second. It covers 6 radians in one minute and the final position after 10 minutes is roughly at the 198-degree mark from the 12 o'clock position.
Step-by-step explanation:
a) Since the minute hand rotates counterclockwise, this is the direction it rotates in.
b) The minute hand rotates at a rate of 0.1 radian per second. In 1 minute (60 seconds), it rotates 60 × 0.1 = 6 radians.
c) The initial position at the 15-minute mark corresponds to 90 degrees (a quarter of a circle from the top of the hour). Therefore, the initial position in radians is π/2 radians (since π radians is 180 degrees).
d) In 10 minutes (600 seconds), the minute hand rotates 600 × 0.1 = 60 radians. However, since a full revolution is 2π radians, we can calculate the final position by removing full revolutions and considering the remainder:
Total rotations in 60 radians = 60 / (2π) ≈ 9.55
Since 9 full rotations bring us back to the start, we consider only the 0.55 of a rotation. This fraction of a revolution is 0.55 × 360 degrees = 198 degrees.
Therefore, the final position after 10 minutes is roughly at the 198-degree mark from the 12 o'clock position.