Q.) Condition for maximum range (R) for a projectile thrown UP/DOWN the inclined plane :
R = [ u cos alpha x 2u sin alpha / g cos theta ] + – [ 1 x g sin theta/2 x 4u^2 sin^2 alpha / g^2 cos^2 theta ].
Where, constants are : u, 2, g, theta.
Also : u cos alpha is the component of Initial velocity, 2u sin alpha / g cos theta is Time of flight(T), g sin theta is component of final velocity, and 4u^2 sin^2 alpha / g^2 cos^2 theta is square of the Time of flight(T)
Now, After simplification of this formula( by derivation), we get :
Maximum Range (R) = u^2 / g(1 + - sin theta).
Where theta is angle of inclination, plus ➕ sign is for projectile up the plane, and minus ➖ sign is for projectile down the plane.
SHOW THE DERIVATION OF THE FORMULA.
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