Question

The figure shows two possible paths for

negotiating an unbanked turn on a

horizontal portion of a race course. Path

− follows the centerline of the road

and has a radius of curvature #= 85 ,

while path − uses the width of the

road to good advantage in increasing the

radius of curvature to $= 200 . If the

drivers limit their speeds in their curves

so that the lateral acceleration does not

exceed 0.8, determine the maximum

speed for each path.

Answer 1

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Step-by-step explanation:

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Answer 2

The maximum speed for Path 1 is approximately 8.246 m/s, while the maximum speed for Path 2 is approximately 12.65 m/s.

To determine the maximum speed for each path, we need to consider the maximum lateral acceleration allowed, which is 0.8. The lateral acceleration is related to the radius of curvature of the path and the speed of the vehicle. The formula for lateral acceleration is:

lateral acceleration = (velocity^2) / radius of curvature

Let's calculate the maximum speed for each path using this formula:

For Path 1 (radius of curvature = 85 m):

0.8 = (velocity^2) / 85

Solving for velocity, we get:

velocity^2 = 0.8 * 85

velocity^2 = 68

velocity = sqrt(68)

velocity ≈ 8.246 m/s

Therefore, the maximum speed for Path 1 is approximately 8.246 m/s.

For Path 2 (radius of curvature = 200 m):

0.8 = (velocity^2) / 200

Solving for velocity, we get:

velocity^2 = 0.8 * 200

velocity^2 = 160

velocity = sqrt(160)

velocity ≈ 12.65 m/s

Therefore, the maximum speed for Path 2 is approximately 12.65 m/s.