The speed of a car is increased by $10\%$. If the angle of banking remains constant,the radius of the turn must be changed from $20 \ m$ to ........ $m$.

$A$ 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 maximum speed of the car is ............ $m/s$ $[g = 10\,m/s^2]$.

$A$ circular freeway entrance and exit are commonly banked to control a moving car at $14 \ m/s$. To design a similar ramp for $28 \ m/s$, one should:

$A$ road is $10\, m$ wide. Its radius of curvature is $50\, m$. The outer edge is raised above the inner edge by a distance of $1.5\, m$. This road is most suited for the velocity of ........ $m/s$. (in $.5$)

$A$ road is $10 \text{ m}$ wide. Its radius of curvature is $50 \text{ m}$. The outer edge is above the inner edge by a distance of $1.5 \text{ m}$. This road is most suited for the velocity $[g = 9.8 \text{ m/s}^2]$: (in $\text{ m/s}$)

The safe speed of a vehicle over a smooth banked road of radius $150\ m$ is $10\ m/s$. If the width of the road is $7.5\ m$,the height of the outer edge is: (in $m$)