A car of mass $1000\,kg$ negotiates a banked curve of radius $90\,m$ on a frictionless road. If banking angle is $45^o$ , the maximum speed of car is ............ $m/s$ $[g = 10\,m/s^2]$
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$\tan \theta=\frac{\mathrm{v}^{2}}{\mathrm{Rg}}$
$\tan 45^{\circ}=\frac{\mathrm{v}^{2}}{90 \times 10}$
$\mathrm{v}=\sqrt{900}=30 \mathrm{m} / \mathrm{s}$
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