MHB Solving Minute Hand Distance from Ground Graph Problem

[jshayhsei]

I'd like to know how to solve this. I'm pretty lost as to how to solve this. I want to say that the graph would look periodic because of the graph of the time would go down and then go back up again, but I really don't have anything concrete.

The question states:

The circular clock has a diameter of 14 inches and its minute had has length 6 inches. It is placed on the wall so that the center of the clock is 66 inches above the ground. Which of the following graphs could represent the distance from the tip of the arrow of the minute hand to the ground with respect to time from 10 a.m. to 11 a.m.?

View attachment 8815

 

[Evgeny.Makarov]

Hi, and welcome to the forum.

Can you figure out the initial position (height above the ground) of the minute hand tip at 10 a.m.? Also, do you know what cosine is and what its graph looks like?

 

[HallsofIvy]

(A) isn't possible because the minute had will have returned to its original height after 60 minutes.
(C) isn't possible because it has straight lines while the minute hand in moving in a circle.
That leaves (B) and (D) and the most obvious difference between the is that (B) is "smooth" while (D) has a cusp at the bottom. (D) implies a sudden change in direction which cannot be the case in circular motion.