A car is traveling around a horizontal circular track with radius r = 210 m as shown. It takes the car t = 50 s to go around the track once. The angle θA = 29° above the x axis, and the angle θB = 65° below the x axis.
To answer the question, we need to find the velocities of the car at points A and B. We can use the centripetal acceleration formula:
a = (v^2) / r
where a is the centripetal acceleration, v is the velocity, and r is the radius of the circular track. Since the car is not changing its speed, we can assume that the magnitude of the velocity at points A and B is the same.
First, let's find the centripetal acceleration at point A. We can use the equation:
aA = (vA^2) / r
Since we know the radius of the track (r = 210 m) and the time it takes the car to go around the track once (t = 50 s), we can calculate the speed (vA) at point A using the formula:
vA = (2 * π * r) / t
Substituting the values, we get:
vA = (2 * π * 210) / 50
Now, let's find the centripetal acceleration at point B using the same formula:
aB = (vB^2) / r
To find the speed (vB) at point B, we can use the formula:
vB = (2 * π * r) / t
Substituting the values, we get:
vB = (2 * π * 210) / 50
Now we have the velocities (vA and vB) at point A and point B, respectively.