3. (from Web-Assign) Two cannons are mounted as shown below and rigged to fire simultaneously. They are used in circus acts in which two clowns serve as human cannonballs The clowns are fired toward each other and collide at a height of $h = 1$ m above the muzzles of the cannons. Clown A (at left) is launched at an angle of $\theta_A = 72^\circ$ with a speed $v_A = 8$ m/s. The horizontal separation between the clowns as they leave the cannons is $d = 6$ m. (a) Find the x- and y-components of Clown A's initial velocity. Call these $v_{Ax}$ and $v_{Ay}$. (b) Find the x- and y-components of Clown B's initial velocity, and from these, the initial speed and launch angle of Clown B (If there is more than one solution, discuss the meaning of the two solutions, drawing a sketch of what happens in each case.) (c) What happens if you raise the height $h$ at which the Clowns collide? For the given data, is there a height $h_{max}$ above which it is not possible to have the clowns collide? If so, find this $h_{max}$.
