Final answer:
When a bus moving North at a uniform speed of 50 km/h makes a 90-degree turn, its speed remains constant but its velocity changes due to the change in direction. The resultant velocity can be calculated using vector algebra, as the Pythagorean theorem when the directions are perpendicular. The increase in velocity during the turning process is 20.710 km/h.
Step-by-step explanation:
The question essentially requires an understanding of the concept of velocity, particularly how a change in direction influences it.
The speed of the bus remains consistent at 50 km/h; however, velocity is a vector quantity that considers both magnitude (speed) and direction. Therefore, when the bus turns 90 degrees, there is a change in direction and hence a change in velocity, even though the uniform speed remains constant.
Therefore, the change in velocity can be calculated using vector algebra. When two vectors with the same magnitudes (50 km/h each) are perpendicular to each other (a 90-degree angle between the Northward and Eastward/Westward direction), the magnitude of the resultant vector can be found using the Pythagorean Theorem. So, new velocity becomes √((50)² +(50)²) = √5000 = 70.710 km/h.
The increase in velocity is calculated by subtracting the initial speed from the final velocity, hence 70.710 km/h - 50 km/h = 20.710 km/h. So, the increase in velocity in the turning process is 20.710 km/h.
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