Question

in a car race feild(round track that is 500m diameter an observer was starting point and the race started a red car finished 5 laps in 30 minutes write a sin function to determine the distance between the observer and the red car at the minute graph the function.​

Answer 1

Distance between the observer and the red car is
`250 Sin (\pi)/(3)t`

Explanation:

Diameter of field = 500 m

Radius of field =
`(Diameter)/(2)=(500)/(2)=250 m`

Let R be the radius and the speed at which the car completes race be w

So,
`w=(2\pi)/(T)`

Car finished 5 laps in minutes = 30

Car finished 1 lap in minutes =
`(30)/(5)=6`

So,
`w=(2\pi)/(6)=(\pi)/(3)`

Refer the attached figure

Angle between car and observer = wt

So, Distance between the observer and the red car is give as A sin wt

So, Distance between the observer and the red car=
`250 Sin (\pi)/(3)t`