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A 1325 kg car and a 2050 kg pickup truck approach a curve on a highway that has a radius of 255 m. At what angle should the highway engineer bank this curve so that vehicles traveling at 75.0 mi/h can safely round it regardless of the condition of their tires

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onyebuchinnaji

Answer:

the banking angle of the road is 24.2⁰

Explanation:

Given;

speed of the vehicles considered, v = 75 mi/h

Speed in m/s ⇒ 1 mi/h --------> 0.44704 m/s

                         75 mi/h --------> ?

=   75 x 0.44704 m/s = 33.528 m/s

radius of the curve, r = 255 m

The banking angle of the road is calculated as;

[tex]\theta = tan^{-1} (\frac{v^2}{rg} )\\\\\theta = tan^{-1} (\frac{33.528^2}{255\times 9.8} )\\\\\theta = tan^{-1}(0.44983)\\\\\theta =24.2^0[/tex]

Therefore, the banking angle of the road is 24.2⁰

pstnonsonjoku

The angle of banking is 24 degrees.

What is the angle of banking?

As a driver approaches a bend two equal and opposite forces act on him which are the centripetal force and the centrifugal force. The driver will have to ben through a certain angle called the angle of banking to avoid falling off.

The angle of banking depends on the speed of the vehicle and the radius of the curve.

θ = v^2/rg

speed = 75.0 mi/h or 33.5 m/s

r = 255 m

g = 9.8 ms-1

θ = tan-1 (33.5 m/s)^2/ 255 m × 9.8 ms-1

θ =   tan-1(1122.3/2499)

θ =  24 degrees

Learn more about banking: https://brainly.com/question/12134554

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