3. (26 Marks) The figure to the right shows a small cannon that can fire balls (B) with an initial speed $v_{OB}$ at a fixed angle $\theta = 53.0^\circ$ above the positive x-axis, at the top right edge of a building. It takes B 4.00 s to reach the ground.\\
a) Find $v_{oy,B}$, then deduce the values of $v_{OB}$ and $v_{ox,B}$.\\b) Find $h_{max}$, the maximum height above the ground that B can reach.\\c) Show that B hits the ground at a horizontal distance d = 21.4 m.\\d) What should be the new value of $v_{OB}$ so that the horizontal range of B is R = 2.30 d?\\At the instant B was launched, a car C on the ground directly below B starts to accelerate to the right with a constant acceleration $a_c = 4.22 m/s^2$.\\e) Find the magnitude and direction of $\vec{a}_{BC}$, the acceleration of B with respect to C.\\f) What should be the new value of $v_{OB}$ so that B will hit C on the ground?