To solve this problem, we can use the physics concept of banking of roads. The formula to find the speed (v) is:

v = sqrt(r * g * tan(θ))

where:
- r is the radius of the curve (354 m in this case)
- g is the acceleration due to gravity (approximately 9.8 m/s² on Earth)
- θ is the bank angle (30.3° in this case)

First, we need to convert the bank angle from degrees to radians because the trigonometric functions in most calculators use radians.

1 degree = π/180 radians

So, 30.3° = 30.3 * π/180 = 0.529 rad

Now we can substitute the values into the formula:

v = sqrt(354 m * 9.8 m/s² * tan(0.529 rad))

Calculate the value inside the square root:

= sqrt(3471.2 m²/s² * 0.636)

= sqrt(2208.67 m²/s²)

Finally, take the square root to find the speed:

v = 47 m/s

So, the track has been designed to accommodate race cars traveling at a speed of 47 m/s.

Question

To solve this problem, we can use the physics concept of banking of roads. The formula to find the speed (v) is:

v = sqrt(r * g * tan(θ))

where:
- r is the radius of the curve (354 m in this case)
- g is the acceleration due to gravity (approximately 9.8 m/s² on Earth)
- θ is the bank angle (30.3° in this case)

First, we need to convert the bank angle from degrees to radians because the trigonometric functions in most calculators use radians.

1 degree = π/180 radians

So, 30.3° = 30.3 * π/180 = 0.529 rad

Now we can substitute the values into the formula:

v = sqrt(354 m * 9.8 m/s² * tan(0.529 rad))

Calculate the value inside the square root:

= sqrt(3471.2 m²/s² * 0.636)

= sqrt(2208.67 m²/s²)

Finally, take the square root to find the speed:

v = 47 m/s

So, the track has been designed to accommodate race cars traveling at a speed of 47 m/s.

Knowee AI · Accepted Answer