Shadow doesn't always follow you!

A small block can move in a straight horizontal line ABAB.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:

aN=cvR(2Rtvt2),aT=R(vtR)vde(2Rtvt2)fga_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|c|+|d|+|e|+|f|+|g|


Details and Assumptions

  • As shown in figure vv is the constant along ABAB.

  • Given Figure is top view of the setup.

  • c,d,e,f,gc,d,e,f,g are natural numbers and de,fg\frac{d}{e} ,\frac{f}{g} are in simplest forms.

  • aN,aTa_N,a_T represent normal and tangential accelerations respectively.

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

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