Question

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 3.0 m/s and the track has a diameter of 200 meters .
A) How many seconds ahead of jogger B does jogger A arrive?
B) How do their travel distances compare? in meters
C) How do their displacements compare? in meters north
D) How do their average velocities compare? in m/s north

Compare, give two answers for each question to compare them

Answer 1

here,

speed of joggers , v = 3 m/s

diameter of the circular track , d = 200 m

radius , r = 100 m

A)

the time ahead of jogger B does jogger A arrive is t = (pi *r - 2* r)/v

t = (pi *100 - 2 *100)/3

t = 38 s

the time difference between the joggers is 38 s

B)

distance of differenec between the joggers , d = pi *r - 2 *r

d = 114 m

C)

the diplacement of both the joggers is same

as the displacement is the shortest distance

the displacement for the both the joggers is 2*r

or 200 m

D)

average velocity of jogger A , vA = 2*r / t

vA = 3 m/s

avergae velocity for jogger B , vB = 2 * r/(pi *r/v)

vB = 2 *v/pi

vB = 1.91 m/s

the velocity of jogger B is 1.91 m/s