66When, the man covers a distance s along the circle, the angle subtended by the arc which he has covered is θ = s/R where R is the radius of the circle. Accordingly, the man's shadow covers a distance x along the wall is given by
tan θ = xR
from where we get
x = R tan (s/R).
Differentiating w.r.t time, we have
dx/dt = sec2(s/R) ds/dt
Note that u = ds/dt is the man's speed along the circle and v= dx/dt is the shadow's speed along the wall. So when he covers 1/8th of the track s = 2Ï€R/8, so that
v = sec2(Ï€/4) u = 2u = 20 km/hr
