Question

A toy racecar races along a circular race track that has a radius of 29 meters. The racecar starts at the 3-o'clock position of the track and travels in the CCW direction. Suppose the car has swept out 2.55 radians since it started moving.

The racecar is how many radius lengths to the right of the center of the race track?

radius lengths   

The racecar is how many meters to the right of the center of the race track?

meters   

The racecar is how many radius lengths above the center of the race track?

radius lengths   

The racecar is how many meters above the center of the race track?

meterss   

Answer 1

soln: we have radius of circular path= 29 meter, starting point is 3 o'clock position i.e positive x axis

car has swept out 2.55 radians so  θ=2.55 radians

we know that any coordinate on circular path = (rcosθ, rsinθ) so,

=> radius lengths to the right of the center of the race track= (rcosθ)/r = cosθ = cos(2.55) = -0.83 radius

hence now the car is 0.83 radius left to the center of race track.

=> lengths to the right of the center of the race track= (rcosθ) meter = rcosθ = 29cos(2.55) = -24.072 meter

hence now the car is 24.072 meter left to the center of race track.

=> radius lengths to the above of the center of the race track= (rsinθ)/r = sinθ = sin(2.55) = 0.5578 radius

hence now the car is 0.5578 radius above to the center of race track.

=> lengths to the above of the center of the race track= (rsinθ) meter = rsinθ = 29sin(2.55) = 16.1728 meter

hence now the car is 16.1728 meter above to the center of race track.