Question

A horse trainer is standing at the edge of a circular watching a horse and rider gallop counter clockwise around the perimeter of the track. Given that the track is 120 feet in diameter. How fast is the distance s between the trainer and the horse increasing 2pi seconds after the horse passes the trainer, if the horse is galloping at a speed of 20feet/second
Please, help

Answer 1

@jhonyy9

Answer 2

do you have any idea for it ?

Answer 3

I think the angle is from 0 to 2pi, and the distance between the horse and the trainer is from 0 to 120

Answer 4

the speed of horse is 20 feet/sec. and the diameter is 120 feet

yes right

yes the distance from zero to 120 increasing and vice-versa

yes ?

Answer 5

But I don't get what "the distance increasing 2pi seconds" mean

Answer 6

hope you know that pi/2 =90 degree

yes ?

so than pi = 180 degree

so 2pi mean 360 degree what is the circumference angle of a circle

yes ?

Answer 7

yes, then?

Answer 8

but it is "2pi seconds"

Answer 9

how it is used in this case?

Answer 10

oh, is it :
the circumference of the circle is 120pi. and the horse gallops at 20ft/second. Hence it needs 6pi seconds to finish one cycle. Hence at 2pi seconds. it is finish 1/3 of the circumference

Answer 11

use the law of cosines

\(s^2 = r^2 + r^2 - 2 r r \cos \omega t\) etc
\(\omega = \dfrac{v}{r}\)

Answer 12

That is at the point of 120 degree. and we find the distance between it with the trainer. Am I right?

Answer 13

oh, yes. Thanks @IrishBoy123

Answer 14

mp!