A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the bankin

Question

A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is $45^{\circ}$, the safe speed of the car is (Take $g=10 \mathrm{~m/s}^2$)

Professor PC Thomas Classes · Answer

On a frictionless banked road, the safe speed is given by $v = \sqrt{R g 	an 	heta}$. Substitute $R = 90 \mathrm{~m}$, $	heta = 45^{\circ}$, and $g = 10 \mathrm{~m/s}^2$: $v = \sqrt{90 	imes 10 	imes 	an(45^{\circ})} = \sqrt{900 	imes 1} = 30 \mathrm{~m/s}$.