2. A particle P is fired from an origin O, which is at a distance L from the foot of a vertical cliff (AB)| height H. P is fired with

speed U at an angle 0 to the horizontal and lands at a point C (see diagram You may neglect the effects of air resistance and assume that the gravitational field is g=-gk,here g is a constant and k is a unit vector (shown in the diagram). If the position of P relative to O is r(t), explain (in one sentence) why the equation of motion is f = -gk. Starting from the equation of motion above with r = x(t)i+ y(t)j, solve for z(t) and y(t). Hence obtain an expression for the time, T, at which the particle arrives at C in terms of U, 0, g and H;find the distance BC in terms of T, U, 0 and L. If the path of P passes through the point B, then show that the firing angle 0 can be determined from a quadratic equation for the quantity tan 6. (You are not required to solve the quadratic equation.)