A horse is tied to a rope of length 5 cm and the other end of the rope is tied to a pole. Find the displacement and the distance travelled by the horse in the following cases (i) When the horse makes half revolution along a circular path. (ii) When it makes one full revolution (iii) When it makes (3)/(4) th of the revolution.

A horse is tied to a rope of length 5 cm and the other end of the rope

1.	A horse is tied to a rope of length 5 cm and the other end of the rope is tied to a pole. Find the displacement and the distance travelled by the horse in the following cases (i) When the horse makes half revolution along a circular path. (ii) When it makes one full revolution (iii) When it makes (3)/(4) th of the revolution.
Answer» Solution : (i)Half revolution along the circular path. Distance travelled by the horce `=(2pir)/(2)=pir=pixx55pim` Displacment of the horse = DIAMETER of the circular path, `bar(H_(1)H_(2))` = 10m from `H_(1)"to" H_(2)` (II) When the horse MAKES full revolution Distance traveleld by the horse = circumference of the circular path `=2pir=2pixx5=10m` Displacement of the horse= zero (Sicne INITIAL and FINAL position of the horse conincide) (III) When the horse makes `(3)/(4)` th of the revolution Distane travelled by the horse `=(3)/(4)` th of the circumference of the circle = `(3)/(4)(2pir)` `(3)/(2)xxpixx5=(15)/(2)pi=7.5pi m` Displacment of the horse `= bar (H_(1) H_(2))` `\|bar(H_(1)H_(2))\|` = shortest distance between `H_(1) and H_(2)` `=sqrt(5^(2)+5^(2))= sqrt(25+25)=sqrt(50)` `=5sqrt(2)mH_(1) "to"H_(2)`