An inclined plane and banked curve problem can be approached in the following way:

The formula to remember, which is not included on the HSC formula sheet is the following:

Most questions encountered can be solved with this formula.

Memorize.

Master.

Question 1. [2 marks]

A car is turning an Icey corner banked at 7 degrees with a radius of 0.05 km, what is the cars maximum velocity it can go without skidding out?

Question 2. [3 marks]

A local council is considering building a banked curve, they can build one curve with a angle of 15 degrees and is 150 m radius while the other design has an angle of 16 degrees and a radius of 170 m. Which ramp would be safer and why?

Question 3. [4 marks]

Two cars of the same mass on a planet other then earth take a corner of radius 150 m and an angle of 10 degrees going 45 km/h. What is the maximum speed they could go when taking another corner of angle 15 degrees and a radius of 92 m.