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A point P on the parabool y = ax^2 + bx + c moves so that the rate of change of its abscissa is a constant, k units/s. (a) (i) Find an expression for the rate of change of the gradiënt of the interval from the origin O to P. (ii) Hence find the value of x for which OP is a tangent to the...

A particles is projected at an angle of theta to a wall of height h metres standing on horizontaal ground at a distance c metres from the point of projection O. It just clears the wall at the highest point of its path. Prove that: (a) the speed V of the projection is given by v^2 = g/2h(c^2 +...