Question

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 revolutino along a circular path.
(ii) When it makes onf full revolution
(iii) When it makes `(3)/(4)` th of the revolution.

Answer 1

(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)`