Suppose a ball of mass 0.2kg strikes a free-floating uniform rod (of mass 0.4kg and length 1.2m) a distance of 0.3m from its center of mass at a right angle with initial speed 14 m/s. The ball ricochets off the rod, with final velocity pointing in the opposite direction of its initial velocity, and the rod begins to move and rotate. What is the final speed of the ball, the final speed of the center of mass of the rod, and the final angular velocity of the rod?

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Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. (a) what is the position vector, rtarge t, that originates from the balloon's original position and terminates at the target? put this in terms of h and d, and represent it as a vector using i and j. (b) in terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. your answer should not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.