A beacon that is located a perpendicular distance of 400 m from a point X on the shoreline makes one revolution a minute. How fast does the beam of light sweep along the shoreline at point Y which...

A beacon that is located a perpendicular distance of 400 m from a point X on the shoreline makes one revolution a minute. How fast does the beam of light sweep along the shoreline at point Y which is 300 m down the shore from X?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The beacon that is located a perpendicular distance of 400 m from a point X on the shoreline makes one revolution a minute. The angular velocity of the beacon is `2*pi` radians/minute.

The speed at which the beam of light sweeps along the shoreline at a point Y that is 300 m from the point X is given by the linear velocity at that point.

Use the formula v = `omega*r` where omega is the angular velocity and r is the radius. Here, the radius r is equal to the distance of the point Y from the beacon that is `sqrt(300^2 + 400^2)` = `sqrt 250000` = 500 m. The linear velocity is `omega*r` = `2*pi*500` = `1000*pi` m/min.

The beam of light sweeps the point Y at `1000*pi` m/minute.

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