Answer:
The horse will run a distance of 1.5 times the length of the rope around the pole with the rope tightly stretched.
Step-by-step explanation:
The distance the horse will run around the pole with the rope tightly stretched can be calculated using the formula for the circumference of a circle:
Circumference = 2 × π × radius
Since the horse takes one and a half rounds, we need to multiply the circumference by 1.5 to get the total distance the horse runs around the pole.
Let's assume that the length of the rope is the radius of the circle, and the horse is tied at the center.
Therefore, the distance the horse will run around the pole with the rope tightly stretched is:
Distance = 1.5 × 2 × π × radius
Since the horse is tied with a long rope, we need to use the length of the rope as the radius of the circle.
Let's assume that the length of the rope is 'L'. Then the radius of the circle is equal to L/2π.
Substituting this value in the formula, we get:
Distance = 1.5 × 2 × π × (L/2π)
Simplifying the expression, we get:
Distance = 1.5 × L
Therefore, the horse will run a distance of 1.5 times the length of the rope around the pole with the rope tightly stretched.