Question

In auto Racing turns are banked, which helps the cars travel around the track at high speeds because the angles provide an inward force that helps keep the cars from flying off the track. The Daytona international Speedway in Florida has four banked turns. Use the information given below to find the measurement of angle 3.

m of angle 1 + m of angle 3 + m of angle 4 = 93 degrees
m of angle 2 + m of angle 4 equals 62°
2=3
1=2
A. 31 degrees
B. 41 degrees
C. 51 degrees
D. 61 degrees

Answer 1

The ideal speed to take a 100 m radius curve banked at 65.0°, assuming a frictionless surface, is approximately 45.84 meters per second. This speed is calculated using the centripetal force formula for a frictionless banked curve.

Step-by-step explanation:

To find the ideal speed to take a steeply banked tight curve on a racetrack, we can refer to examples such as the Daytona International Speedway. For instance, to calculate the speed at which a 100 m radius curve banked at 65.0° should be driven if the road is frictionless, we would use the physics of circular motion. Specifically, we use the formula for centripetal force, which in the case of a frictionless banked curve, is provided entirely by the normal force's horizontal component.

The formula to find the ideal speed ("v") for a frictionless banked curve is:

v = √(rg anθ)

Where:

"r" is the radius of the curve (100 m)

"g" is the acceleration due to gravity (9.8 m/s²)

"θ" is the banking angle of the curve (65.0°)

Let's calculate the ideal speed:

v = √(100 m * 9.8 m/s² * tan(65.0°))

v = √(980 * tan(65.0°))

v = √(980 * 2.1445)

v = √(2101.61)

v = 45.84 m/s

So, the ideal speed to take this banked curve is approximately 45.84 meters per second.