Question

A horse is tied to a rope of length 5 m and the order end of the rope is tied to a pole, find the displacement and the distance travelled by the horuse in the following cases.
i. When the horse makes half revolution along a circular path.
ii. when it markes one 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 horse = `(2pir)/2= pir = pixx5 = 5 pi m`
Displacement of the horse = diameter of the circular path `vec(H_(1).H_(2))` = 10 m from ` H_(1) "to" H_(2)`
When the horse makes full revolution
Distance travelled by the horse = cicumference of the circular path = `2 pir = 2pi xx 5 = 10 pi m`
Displacement of the horse= zero( since initial and final position of the horse coincide)
iii. When the horse makes `3/4` th of the revolution
Distance travlled by the horse = `3/4` th of the circumference of the circle ` = 3/4 ( 2 pir)`
` = 3/2 xx pi xx 5 = 15/2 pi = 7.5 pi m`
Displacement of the horse= `3/4`
`|3/4|` = the shortest distance between ` H_(1) and H_(2)`
`3/2`
`5 sqrt2 ` m long ` H_(1) "to " H_(2)`