Spiraling and Tumbling

Geometry Level 4

Two cars are stationed at A and B, as in the above diagram. Car B follows a particular spiral course, which consists of coils which are at a constant width from the coil just wider than itself. For example, the width between the second coil and the outer most coil is constant and equal to the width between the second coil and the third coil. Car A starts \(2.7\) km. away from car B. Car A moves in a path which is tangential to the spiral path of car B, but in a straight line. As car A approaches the spiral, it turns and again moves as a tangent to the spiral. Car A continues doing this until it reaches C, a point in the second-innermost coil, while car B continues it's path until it reaches D, the end of the spiral. If the distance travelled by car B is \(55\pi\) km., and car A wants to reach C before car B reaches D, then what is the minimum speed car A must go, if car B's speed is \(10\) km/h? Give answer as nearest integer, in km/h.

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