Solve Easy Vector Problem: Find Displacement of Clock Hands from 3pm-6pm

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In summary, the conversation was about finding the displacements of the tips of a wall clock's minute and hour hands using a Cartesian coordinate system. The hour hand has a length of 0.23 m and the minute hand has a length of 0.45 m. The positive x-axis points to 3 o'clock and the positive y-axis points to 12 o'clock. The displacement of the minute hand is 0 and the displacement of the hour hand can be calculated using the Pythagorean theorem. However, it is also possible to calculate their angular displacements.
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whizbang21
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1. A wall clock has a minute hand with a length of 0.45 m and an hour hand with a length of 0.23 m. Take the center of the clock as the origin, and use a Cartesian coordinate system with the positive x-axis pointing to 3 o'clock and the positive y-axis pointing to 12 o'clock. Find the displacements of the tip of each hand (that is, ΔAarrowbolditalic and ΔBarrowbolditalic) when the time advances from 3:00 P.M. to 6:00 P.M. (Aarrowbolditalic and Barrowbolditalic represent the tip of the hour hand and the tip of the minute hand, respectively.)

Let the +y direction be straight up and the +x direction be to the right. Recall the definition of displacement, and remember that positions are vector quantities.

Homework Equations


dont know, tried Pythagorean theorem.

The Attempt at a Solution


the part dealing with the minute hand is obviously 0. but as far as the hour hand, I've tried using the pythagorean theorem to calculate the displacement which would just be sqrt((.23^2)+(.23^2)^2) but apparently that was wrong, or maybe i just put the wrong sign. only have 1 more submission so not about to guess it.
 
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halp
 
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can you calculate their angular displacements?
 

FAQ: Solve Easy Vector Problem: Find Displacement of Clock Hands from 3pm-6pm

1. How do you calculate the displacement of clock hands?

To calculate the displacement of clock hands, you need to find the difference between the starting and ending positions of the hands. In this case, the starting position is 3pm and the ending position is 6pm. You can do this by converting the time to degrees, where 1 hour = 30 degrees and 1 minute = 0.5 degrees. Then, subtract the degree values of the starting position from the ending position to get the displacement.

2. What is the formula for finding the displacement of clock hands?

The formula for finding the displacement of clock hands is: Displacement = (Ending position - Starting position) * (30 degrees/hour) * (1 hour/60 minutes).

3. How do you convert time to degrees for calculating the displacement?

To convert time to degrees, you can use the formula: Degrees = (Hours * 30) + (Minutes * 0.5). For example, to convert 3pm to degrees, you would do (3 * 30) + (0 * 0.5) = 90 degrees.

4. Can you use this method for any time interval on a clock?

Yes, you can use this method for any time interval on a clock. The key is to convert the starting and ending times to degrees and then find the difference between them. Keep in mind that the displacement will be different for clockwise and counterclockwise movements.

5. Are there any other factors to consider when calculating the displacement of clock hands?

One factor to consider is the size of the clock. The degree values for the hour and minute hand may vary for different sized clocks. Additionally, if the clock has a second hand, it may affect the displacement calculation as well.

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