A racecar driving counterclockwise on a circular track with

A race-car driving counter-clockwise on a circular track with a radius of 2.4 miles. The car starts at the 3 o\'clock position and travels at a constant speed of 82 miles per hour. What distance (in miles) has the race-car traveled if the car has swept put an angle of 266 degrees? What is the measure of the angle swept out by the car (in radius) if the car has traveled miles? Define a function, h, that gives the race-car\'s distance above the horizontal diameter of the track (in miles) in terms of the number of hours since the race-car started driving.

Solution

a) angle swept = 266 degrees = 4.64 radians

arc length = radius*theta = 2.4*4.64 = 11.14 miles

distance car travelled = 11. 14 miles

b) Angle = arc length/ radius = 6.8/2.4 = 2.83 radians

c) angular velocity = linear vel/ radius = 82/2.4 = 34.17 rad/ hr

arc length travlled in time t = 82*t

angle subtended at centre = 82t/radius = 82t/2.4 = 34.17t

Distance above horizontal dia : sin(theta) = h/radius

2.4*sin(34.17t) = h(t)