Final answer:
The bug on the clock's second-hand moves 15 cm in 30 seconds, and its vector movement is 15 cm in the negative vertical direction, considering the clock hand’s rotation from 12 to 6 o'clock.
Step-by-step explanation:
If a bug at the tip of a clock's seconds pointer that is 20 centimeters long moves at the speed of 0.5 cm/s, after 30 seconds, to find the bug's vector movement in centimeters, we can calculate the distance traveled linearly along the path of the clock's second hand. Given the bug's speed is 0.5 cm/s, over 30 seconds, the bug will move 0.5 cm/s * 30 s = 15 cm along the second hand's path.
The vector movement is not simply 15 cm, because the second hand of the clock is also moving. The second hand of a clock completes one full rotation, which is 360 degrees, in 60 seconds. Therefore, in 30 seconds, the second hand will rotate through half of this, which is 180 degrees. This means that the bug has moved from pointing at 12 o'clock to pointing at 6 o'clock.
To describe the vector displacement, we must account for both magnitude and direction. The bug started at the 12 o'clock position and ended at the 6 o'clock position. In vector terms, this corresponds to moving 15 cm downward from its original position, assuming downward is the negative direction. Therefore, the vector that represents the bug's displacement is 15 cm in the negative vertical direction.