Question

Two joggers run at the same average speed. Jogger A cuts directly north across the diameter of the circular track, while jogger B takes the full semicircle to meet his partner on the opposite side of the track. Assume their common average speed is 2.80 m/s and the track has a diameter of 160 m A) How many seconds ahead of jogger B does jogger A arrive? B) How do their travel distances compare? C) How do their displacements compare? D) How do their average velocities compare?

Answer 1

To solve this problem, you can use circle geometry, the semicircle is π times as long as the diameter.

therefore –

(a) A takes time, t = d / v = 160 m / 2.8 m/s = 57 s

And B takes 57s * π = 179 s,

This means, A arrives (179 – 57) = 122 seconds ahead of B.

(b) 1:π,

    Or, 160 m : 503 m

(c) displacements are equal at 160 m

(d) For A, V(average) = 2.8 m/s north
And for B, V(average) = 2.8 m/s / π north = 0.89 m/s north. (It took him π times as long)