To find the magnitude of the average velocity, we need to calculate the total displacement and total time taken.
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Total Displacement: The bike rider travels 75 m West and then 75 m North. We can find the resultant displacement using the Pythagorean theorem (\(d = \sqrt{x^2 + y^2}\)) where:
- \(x = 75 , \text{m}\) (West)
- \(y = 75 , \text{m}\) (North)
\[ d = \sqrt{(75 , \text{m})^2 + (75 , \text{m})^2} = \sqrt{5625 + 5625} = \sqrt{11250} \approx 106.07 , \text{m} \]
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Total Time: The total distance traveled is the sum of the two legs of the trip: \[ \text{Total distance} = 75 , \text{m} + 75 , \text{m} = 150 , \text{m} \]
The speed of the bike rider is 1.5 m/s. To find the time, we use the formula: \[ \text{Time} = \frac{\text{Total distance}}{\text{Speed}} = \frac{150 , \text{m}}{1.5 , \text{m/s}} = 100 , \text{s} \]
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Average Velocity: The average velocity is defined as the total displacement divided by the total time. \[ \text{Average velocity} = \frac{\text{Total displacement}}{\text{Total time}} = \frac{106.07 , \text{m}}{100 , \text{s}} = 1.0607 , \text{m/s} \]
Rounded to two decimal places, the magnitude of the average velocity is approximately 1.06 m/s.
None of the provided options exactly match this result, but it closely approximates 1.1 m/s. Therefore, the best choice among the given options is:
1.1 m/s.