A car is traveling around a horizontal circular track with radius r = 270 m as shown. It takes the car t = 66 s to go around the track once. The angle θA = 19° above the x axis, and the angle θB = 56° below the x axis.

1What is the magnitude of the car’s acceleration?

What are these angles?

To find the magnitude of the car's acceleration, we need to use the formula for centripetal acceleration:

Acceleration (a) = v^2 / r

Where:
a = acceleration
v = velocity
r = radius of the circular track

First, let's find the velocity of the car. We know that it takes the car 66 seconds to go around the track once, so we can calculate the speed:

Speed (v) = distance / time

The distance traveled in one complete circle is equal to the circumference of the circular track, which is given by:

Circumference = 2 * π * r

Plugging in the values for radius (r = 270 m) and time (t = 66 s), we can find the velocity:

v = (2 * π * r) / t

Once we have the velocity, we can calculate the acceleration using the formula mentioned earlier:

a = v^2 / r

Substituting the value of velocity (v) and radius (r), we can find the magnitude of the car's acceleration.