The roadway bridge over a stream is in the form of an arc of a circle of radius 50 m. What is the maximum speed with which a car can cross the bridge without leaving the ground at the highest point?

Explanation

Suppose the car is moving with a speed v on the bridge so that it can cross the bridge without leaving the ground at the highest point.
If the normal force at the highest point on the bridge is F, then
`mg - F = (mv^(2))/(r )`
For the maximum speed of the car, at the highest point on the bridge, F = 0
`therefore " " (mv^(2))/(r ) = mg " " or, " " v^(2) = rg`
or,`" " v = sqrt(rg) = sqrt(50 xx 9.8)`
= 22 m`cdot s^(-1)`