A cyclist moves along a semicircular track of radius 70m from point P to the diametrically opposite point Q and then returns to P along the straight chord QP.
a. (i) Find the distance travelled by the cyclist for the journey P→Q.
b. (ii) Find the total distance and the net displacement for the complete journey P→Q→P.
c. (iii) Prove algebraically that the net displacement for any closed path that brings an object back to its starting point is zero.