A70kg car drives through a curve with radius 50m. what is the minimum angle the road should be tilted to keep the car on the road at a speed of 80km/h and the coefficient of friction is near 0 on a rainy day.

when car moves along a circular path then centripetal force for taking turn will be provided by the component of normal force

Let the road is tilted by some angle

so force equations are given as

now divide two equations

now as it is given to us that

now we have

so it is inclined at an angle of 45 degree

i will answer your question if you answer mine

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft