There is a parabolic-shaped bridge across the river of width 10 meter. The highest point of the bridge is 4m meter above the level of bank. A car of mass 72kg is crossing the bridge at a constant speed 5m/s.If the force (in Newton) exerted on the bridge by car when it is at the highest point ‘P’ of the bridge is $18 x$ newton. The value of $x$ is……. (take g=10m/s²)

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answer is 8.

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Detailed Solution

Equation of parabola

$y = k x^{2} y = h = k a^{2} k = (\frac{h}{a^{2}}) y = (\frac{h}{a^{2}}) x^{2} R = \frac{{[1 + {(\frac{d y}{d x})}^{2}]}^{- 3 / 2}}{\frac{d^{2} y}{d x^{2}}} R (x = 0) = (\frac{1}{2 k}) m g - N = \frac{m v^{2}}{R}$

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