Question

An engineer wants to design an oval racetrack such that 3.20×103 lb racecars can round the exactly 1000 ft radius turns at 99 mi/h without the aid of friction. She estimates that the cars will round the turns at a maximum of 175 mi/h. Find the banking angle θ necessary for the race cars to navigate the turns at 99 mi/h without the aid of friction.

Answer 1

Answer:

the angle of banking is 33.3 degree.

Explanation:

speed, v = 99 mi/h = 44.26 m/s  

radius, r = 1000 ft = 304.8 m

g = 9.8 m/s^2

Let the angle of banking is A.

$tan A = \frac{v ^2}{r g}\\\\tan A = \frac{44.26^2}{304.8\times 9.8}\\\\tan A = 0.66\\\\A = 33.3^0$