Final answer:
Using the relationship between linear speed, angular speed, and radius, the average speed of the passenger side front wheel is approximately 24.568 m/s when the driver side wheel's average speed is 24.0 m/s.
Step-by-step explanation:
To solve for the average speed of the passenger side front wheel when the car's driver side front wheel has an average speed of 24.0 m/s while driving around a circular racetrack counterclockwise, we can use the relationship between linear speed, angular speed, and the radius of the circular path.
First, let's find the radius of the circular path by using the given data that a complete circle is traveled every 33.47 seconds. The distance covered by the driver side wheel is the circumference of the track which is equal to the average speed times the time to complete a circle, hence:
Circumference = Speed × Time = 24.0 m/s × 33.47 s
= 803.28 m
To find the radius (r), we use the formula for circumference:
Circumference = 2πr
r = Circumference / (2π) = 803.28 m / (2π) ≈ 127.65 m
Linear speed
and radius are related through the angular speed (ω), which is the same for both wheels as they complete a circle in the same amount of time. Using the formula
v = ωr, where
v is the linear speed and
ω is the angular speed, we can say that the angular speed of the driver side wheel is:
ω = v / r = 24.0 m/s / 127.65 m
≈ 0.188 rad/s
Since both wheels share the same angular speed, the passenger side front wheel's average speed can be found by adding the distance between the wheels to the radius used for the driver side wheel and then using the same angular speed:
rpassenger = rdriver + Distance between wheels = 127.65 m + 3.03 m
= 130.68 m
Now we calculate the average speed of the passenger side front wheel:
vpassenger = ω × rpassenger = 0.188 rad/s × 130.68 m
≈ 24.568 m/s
Therefore, the passenger side front wheel's average speed is approximately 24.568 m/s.