Jumping Jack

Geometry Level 2

Jack is standing at a distance of 1 m from the origin.He covers a distance of 1 m along the circle of the same radius.Then, he jumps onto the circle of radius 2 m and moves a distance of 2 m along the circle of the same radius.He continues to do this process infinite number of times.What is the minimum number of times he has to jump so as to cross the positive x - axis?

8 7 6 360

Rohit Nair by Rohit Nair , 21, India

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2 solutions

Krishna Garg
May 24, 2014

Consider the perimeter of a circle ,and +ve quadrant to cross X-axis,with 1 Meterradius and covering 1 meter along circle it will be 2pai,for next 2 meters it will be 4 pai,then 6 pai thus total 12 pai then next 14 pai,so jumps 7 times to cross the + ve X-axis.

K.K.GARG.India

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Mads I.
Apr 29, 2014

The fraction of a full circle covered in each step r r is r 2 π r \frac{r}{2\pi r} , so he needs 2 π 2\pi steps to cover a full circle and get back to the positive x-axis. Since 6 < 2 π < 7 6\lt 2\pi\lt 7 , 6 is not enough but 7 is more than enough, so 7 it is.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

He jumps only 6 times, then his movement on the next circle carries him over the x-axis.

Guiseppi Butel - 7 years, 1 month ago

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