Shadow doesn't always follow you!

A small block can move in a straight horizontal line \(AB\).Flash lights from one side projects its shadow on a curved vertical wall which has a horizontal cross section as a circle. If tangential and normal acceleration of shadow of the block on the wall as a function of time can be represented as:

\[a_N=\frac{cvR}{(2Rt-vt^2)} \quad , \quad a_T=\frac{R(vt-R)v^{\frac{d}{e}}}{(2Rt-vt^2)^{\frac{f}{g}}}\].

Find \(|c|+|d|+|e|+|f|+|g|\)

Details and Assumptions

  • As shown in figure \(v\) is the constant along \(AB\).

  • Given Figure is top view of the setup.

  • \(c,d,e,f,g\) are natural numbers and \(\frac{d}{e} ,\frac{f}{g}\) are in simplest forms.

  • \(a_N,a_T \) represent normal and tangential accelerations respectively.

  • you can neglect minus sign in accelerations due to directions.


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