Moving along circles

Question

For each natural number $k$. Let $C_k$ denote the circle with radius $k$ centimetres and centre at origin. On the circle $C_k$ a particle moves $k$ centimetres in the counter - clockwise direction. After completing its motion on $C_k$ the particle moves to $C_{k+1}$ in the radial direction. The motion of the particle continues in this manner. The particle starts at $(1,0)$. If the particle crosses the positive direction of the $x$-axis for the first time on the circle $C_n$. What is the value of $n$?

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Robert Z · Accepted Answer · 2017-07-01T07:05:43.220

2

Hint. On each circle the point moves along an arc of $1$ radian. Now a complete revolution is $2\pi\approx 6.28$ radians.

edited Jul 01 '17 at 07:05

answered Jul 01 '17 at 06:57

Robert Z

145,942

Thanks a lot.You helped me successfully solve it:-) – Abcd Jul 01 '17 at 07:09
@Abcd You are welcome! If you are new here take a few minutes for a tour https://math.stackexchange.com/tour – Robert Z Jul 01 '17 at 07:10

Moving along circles

1 Answers1