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Question

A curve has a radius of 50 m and a banking angle (θ) of 15. What is the maximum safe speed for a car on this curve if the road does not offer any friction? Take g=10 m/s2.

A
105(43) m/s
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B
105(23) m/s
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C
1010(25) m/s
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D
105(33) m/s
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Solution

The correct option is B 105(23) m/s
Applying the condition of banking for a frictionless road:
tan θ=v2rg

v2=rgtanθ
=50×10×tan 15
=50×10×tan(4530)
=50×10×tan45tan301+tan45×tan30
=50×10×313+1

Multiply by 31 on both numerator and denominator
v2=500(23)
v=105(23) m/s

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