There are two equal dots, I and II. Both dots are in the same horizontal line, called C, at a distance of 240cm from each other. The dot I expands itself, creating an infinite line, called A, which makes 90 degrees with C. The dot II does the same, but the line created is called A'. The dot I also expands itself to the right, creating another line, called B, that makes a 45 degrees angle with C. At the same time, the dot II starts to expand itself to the left, creating a line, called B', that also makes a 45 degrees angle with C. Dot I expands the line B by 1,2cm each second, and so does dot II to the line B' (their speed on the lines B and B' is **\(v = 1,2 \text{ cm/s}\)**) . Let \( \alpha\) be the time, in seconds, that it takes to both dots meet in their expansions on the lines B and B'. Also, let \( \beta\) be the distance, in centimeters, that the dot II runs on the line B' until it meets the dot I on the line B. Consider \( \epsilon = \alpha + \beta\). What is the value of \( \lfloor\epsilon\rfloor\)?

**Notes and Assumptions**:

Use a protractor on a notebook page to create the lines B and B'. Try to do just as the image. Do **not** use trigonometric measures for the given angles (for real). Also, consider that the initial positions, vertical and horizontal, of both dots is 0 centimeters.

×

Problem Loading...

Note Loading...

Set Loading...