Consider all the possible continuous smooth 2-D curves joining two points on the **ground** ( 'A' and 'B' ) seperatedd by a distance **L** and lying **entirely** in the vertical plane,

Let the curve be described as **y=f(x)** satisfying **f'(0)=1**

and also as has been mentioned f(0)=f(L)

A particle is to be launched along the curve with an initial speed of **u** from A, so as to reach at B,

What is the equation of the curve f(x) so that the curve exerts absolutely no Normal reaction upon the particle at **each** and **every** point on the curve,

if it can be expressed as

\(y=Ax+B{ x }^{ 2 }+C{ x }^{ 3 }+D{ x }^{ 4 }+E{ x }^{ 5 }.......\quad \)

Find the sum of the coefficients (algebraic sum , not sum of magnitudes)

**Details and Assumptions**

1) L= 10

2) g= 10

3) u= 10

3) Neglect buoyancy , viscous drag , size of particle and variation of 'g' with height

(ALL IN SI UNITS)

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