Question

You are a traffic engineer planning a new roundabout. You expect cars to be drving through it with a speed of 7m/s. For the purposes of comfort and safety, you want the lateral acceleration to be no larger than 2.9m/s². How big across should the roundabout be? (Hint: how big across)

Answer 1

Answer: The roundabout should be about 16.7 meters across.

Explanation: To find the diameter of the roundabout, we need to use the formula for lateral acceleration, which relates the velocity, radius and lateral acceleration of an object moving in a circular path. The formula is:

LAT = v^2 / r

where: LAT is the lateral acceleration, v is the velocity of the object or vehicle, and r is the radius of the curve.

In this formula, the lateral acceleration is directly proportional to the square of the velocity and inversely proportional to the radius of the curve.

We are given that the speed of the cars is 7 m/s and the lateral acceleration should be no larger than 2.9 m/s^2. We can plug these values into the formula and solve for r:

2.9 = 7^2 / r r = 7^2 / 2.9 r ≈ 16.7

This means that the radius of the roundabout should be about 16.7 meters. To find the diameter, we simply multiply the radius by 2:

d = 2 * r d = 2 * 16.7 d ≈ 33.4

Therefore, the diameter of the roundabout should be about 33.4 meters, and the roundabout should be about 16.7 meters across.

Hope this helps, and have a great day! =)