Home
Class 12
MATHS
A horse is tied to a post by a rope. If ...

A horse is tied to a post by a rope. If the horse moves along a circular path always keeping the rope tight, and describes `88` metres when it traces `72^@` at the centre, find the length of the rope.

Text Solution

Verified by Experts

The correct Answer is:
70 m
Let the post be at point P and PA be the length of the rope in tight position. Suppose the horse moves along the are AB so that `angle APB=72^@" and are "AB=88m`
Let r be the length of the rope, i.e., PA = r meters.
Now, `theta=72^@=(72xxpi/182)^R`
`=((2pi)/5)^R`
and `s=88m`
`:. theta=("Are")/("Radius")`
`or (2pi)/5=88/r`
`or r=88xx5/(2pi)=70m`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 2.4|4 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 2.5|16 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 2.2|8 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Archives (Matrix Match Type)|1 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

A horse is tied to a post by a rop. If the horse moves along a circular path always keeping the rope stretched and describes 88 metres when it as traced out 72^(@) at the centre, the length of the rope is (take pi = (22)/(7) )

A cow is tied in a pole with a rope. The cow moves in a circular pan keeping rope straight. When it covers a distance of 44 meter an angle of 72° is subtended at the centre. The length of the rope is:

A truck moves along a circular path and describes 100 m when it has traced out 36^(@) at the centre. The radius of the circle is equal to

A particle is moving along a circular path with a constant speed 30m//s . What is change in velociyt of a particle, when it describe and angle of 90^(@) at the centre of the circle

A horse is tied to a rope of length 5 m 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. When the horse makes half revolution along a circular path.

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 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.