To solve this problem, we can use the physics concept of banking of roads. The formula to calculate the angle (θ) at which the road should be banked is:

tan θ = v²/rg

where:
v = speed of the car = 27.0 m/s
r = radius of the curve = 817 m
g = acceleration due to gravity = 9.8 m/s²

Substituting the given values into the formula, we get:

tan θ = (27.0 m/s)² / (817 m * 9.8 m/s²)

Solving this will give us the value of tan θ. To find the angle θ, we need to take the inverse tangent (also known as arctan or tan^-1) of the result.

Let's calculate:

tan θ = (27.0 m/s)² / (817 m * 9.8 m/s²) = 0.945

θ = tan^-1(0.945) = 43.3 degrees

So, the road should be banked at an angle of approximately 43.3 degrees to prevent the car from skidding sideways.

Question

To solve this problem, we can use the physics concept of banking of roads. The formula to calculate the angle (θ) at which the road should be banked is:

tan θ = v²/rg

where:
v = speed of the car = 27.0 m/s
r = radius of the curve = 817 m
g = acceleration due to gravity = 9.8 m/s²

Substituting the given values into the formula, we get:

tan θ = (27.0 m/s)² / (817 m * 9.8 m/s²)

Solving this will give us the value of tan θ. To find the angle θ, we need to take the inverse tangent (also known as arctan or tan^-1) of the result.

Let's calculate:

tan θ = (27.0 m/s)² / (817 m * 9.8 m/s²) = 0.945

θ = tan^-1(0.945) = 43.3 degrees

So, the road should be banked at an angle of approximately 43.3 degrees to prevent the car from skidding sideways.

Knowee AI · Accepted Answer

To solve this problem, we can use the physics concept of banking of roads. The formula to calculate the angle (θ) at which the road should be banked is:

tan θ = v²/rg

where:
v = speed of the car = 27.0 m/s
r = radius of the curve = 817 m
g = acceleration due to gravity = 9.8 m/s²

Substituting the given values into the formula, we get:

tan θ = (27.0 m/s)² / (817 m * 9.8 m/s²)

Solving this will give us the value of tan θ. To find the angle θ, we need to take the inverse tangent (also known as arctan or tan^-1) of the result.

Let's calculate:

tan θ = (27.0 m/s)² / (817 m * 9.8 m/s²) = 0.945

θ = tan^-1(0.945) = 43.3 degrees

So, the road should be banked at an angle of approximately 43.3 degrees to prevent the car from skidding sideways.

A highway curve has a radius of 817 m. At what angle should the road be banked so that a car traveling at 27.0 m/s (60.4 mph) has no tendency to skid sideways on the road?

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