Question

calculatr the max. speed with which car can be driven safely along a curved road of radius 30 m and banked at 30 degrees with the horizontal ....g is 9.8m/s^2

Answer 1

Let the maximum safe speed be v.

Angle at which the road is banked = 30°

Radius of the curve (r) = 30 m

Acceleration due to gravity (g) = 9.8 m/s^2

For a safe turn:

tan 30° = $\frac{v^2}{rg}$

v = $\sqrt{ tan 30 \times r \times g}$

v = $\sqrt{0.577 \times 30 \times 9.8}$

v = 13.02 m/s

Hence, the safe maximum speed at which we can take turn is 13.02 m/s