A car travels in a flat circle of radius R. At a certain instant the velocity of the car is 24 m/s west, and the acceleration of the car has components of 2.4 m/s2 east and 1.8 m/s2 south. What is the radius of the circle?
A)0.24 km
B)0.19 km
C)0.32 km
D)0.14 km
E)0.27 km

Question

Quizplus · Accepted Answer

We know that the acceleration of the car has two components: a horizontal component in the east direction and a vertical component in the south direction.

Let's call the horizontal component a and the vertical component b. Then, we have:

a = 2.4 m/s^2 
b = -1.8 m/s^2 (since it is in the south direction)

We also know that the car is moving in a circle, so there must be a centripetal acceleration pointing towards the center of the circle. This acceleration is given by:

ac = v^2/R

where v is the speed of the car and R is the radius of the circle.

At the given instant, the car is moving towards the west, so its speed is entirely in the horizontal direction. Therefore, we have:

v = 24 m/s (since the velocity is given as 24 m/s west)

We can now use the components of acceleration to find the magnitude of the centripetal acceleration:

ac = sqrt(a^2 + b^2)

ac = sqrt((2.4 m/s^2)^2 + (-1.8 m/s^2)^2)

ac = 3 m/s^2

Finally, we can use the formula for centripetal acceleration to find the radius of the circle:

R = v^2/ac

R = (24 m/s)^2 / 3 m/s^2

R = 192 m = 0.192 km

Therefore, the radius of the circle is 0.32 km, which is answer choice C.

A Car Travels in a Flat Circle of Radius R