# Solving Minute Hand Distance from Ground Graph Problem

• MHB
• jshayhsei
In summary, the question asks which graph represents the distance from the tip of the minute hand to the ground over the course of an hour. The options (A) and (C) can be eliminated, leaving options (B) and (D). However, (D) is not possible as it implies a sudden change in direction, which is not possible in circular motion. Therefore, (B) is the correct graph.
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.?

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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?

(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.

## 1. How do you solve the minute hand distance from ground graph problem?

To solve the minute hand distance from ground graph problem, you need to first determine the angle formed by the minute hand and the ground at any given time. This can be done by using the formula: angle = (minute hand position / 60) * 360. Once you have the angle, you can use trigonometry to calculate the distance from the ground.

## 2. What is the purpose of solving the minute hand distance from ground graph problem?

The purpose of solving this problem is to determine the height of an object, such as a building or a tree, by using the shadow cast by the minute hand of a clock. This can be useful in situations where it is difficult to directly measure the height of an object.

## 3. What are the key concepts involved in solving the minute hand distance from ground graph problem?

The key concepts involved in solving this problem include understanding angles, trigonometry, and the relationship between the position of the minute hand and the height of an object. It is also important to have a basic understanding of graphing and interpreting data.

## 4. Can this problem be solved using different types of clocks?

Yes, this problem can be solved using different types of clocks as long as they have a minute hand and the same time measurement system (e.g. 12-hour or 24-hour). The key is to accurately measure the position of the minute hand and use the correct formula to calculate the angle.

## 5. Are there any real-world applications for solving the minute hand distance from ground graph problem?

Yes, there are many real-world applications for this problem. For example, it can be used in architecture and construction to estimate the height of a building or in forestry to estimate the height of a tree. It can also be used in navigation and surveying to calculate distances and angles.

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