An old person moves on a semi-circular track of radius 40.0 m during a morning walk. If he starts at one end of the track and reaches the other end, find the distance covered and the displacement of the person.
Answer (2)
The problem involves calculating the distance and displacement of a person walking on a semi-circular track.
Distance is calculated as the length of the semi-circular arc: π r .
Displacement is calculated as the diameter of the semi-circle: 2 r .
With a radius of 40.0 m, the distance is approximately 125.66 m and the displacement is 80.0 m. D i s t an ce = 125.66 m , D i s pl a ce m e n t = 80.0 m
Explanation
Problem Analysis The person walks on a semi-circular track, starting at one end and reaching the other. We need to find the total distance covered and the displacement. The radius of the semi-circular track is given as 40.0 m.
Calculate the Distance The distance covered is the length of the semi-circular arc. The formula for the circumference of a full circle is 2 π r , where r is the radius. Since the track is a semi-circle, the distance covered is half of the circumference, which is π r .
Calculate the Displacement The displacement is the shortest distance between the initial and final points. In this case, it's the straight line connecting the two ends of the semi-circle, which is the diameter of the circle, or 2 r .
Substitute the Radius Given the radius r = 40.0 m, we can calculate the distance and displacement:
Distance = π r = π × 40.0 ≈ 125.66 m
Displacement = 2 r = 2 × 40.0 = 80.0 m
Final Answer Therefore, the distance covered by the person is approximately 125.66 m, and the displacement is 80.0 m.
Examples
Understanding distance and displacement is crucial in sports. For example, when a runner completes a 400m track, the distance covered is 400m, but the displacement is zero because they end up at the starting point. Similarly, in navigation, knowing the displacement helps determine the shortest route to a destination, while the distance helps estimate travel time.
The distance covered by the person walking on the semi-circular track is approximately 125.66 meters, while the displacement from the starting to the ending point is 80.0 meters. Distance measures the actual path taken, whereas displacement is the direct line between those two points.
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