5. A car of mass \(m\) moves in a circular path of radius 75 m round a bend in a road. The maximum speed at which it can move without slipping sideways on the road is \(21 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Given that this section of the road is horizontal,

1. show that the coefficient of friction between the car and the road is 0.6 . The car comes to another bend in the road. The car's path now forms an arc of a horizontal circle of radius 44 m . The road is banked at an angle \(\alpha\) to the horizontal, where \(\tan \alpha = \frac { 3 } { 4 }\). The coefficient of friction between the car and the road is again 0.6. The car moves at its maximum speed without slipping sideways.
2. Find, as a multiple of \(m g\), the normal reaction between the car and road as the car moves round this bend.
3. Find the speed of the car as it goes round this bend.