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.

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