The car drove 500 m along a straight horizontal road. Then he drove over the bridge, which is an arc of a circle

| August 17, 2021 | education

The car drove 500 m along a straight horizontal road. Then he drove over the bridge, which is an arc of a circle (radius of a circle of 500 m) with an opening angle of 600 and then drove another 500 m in a straight line. Determine the path traveled by the car and the modulus of its movement.

Given: S1 (first segment, straight line) = 500 m; R (radius of a circle, bridge) = 500 m; α (opening angle) = 60º; S3 (third segment, straight line) = 500 m.

1) Distance covered: S = S1 + S2 (length of the arc of a circle) + S3 = S1 + Π * R * α / 180º = 500 + 3.14 * 500 * 60º / 180º + 500 = 500 + 523.3 + 500 = 1523.3 m.

2) Movement module: S = S1 + S2 (chord length) + S3 = S1 + 2 * R * sin (α / 2) + S3 = 500 + 2 * 500 * sin 30º + 500 = 500 + 500 + 500 = 1500 m.

Answer: The distance covered is 1523.3 m; movement – 1500 m.



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