Two boys are sliding toward each other on a frictionless, ice-covered parking lot. Jacob, mass 45 kg, is gliding to the right at 7.83 m/s, and Ethan, mass 31.0 kg, is gliding to the left at 10.1 m/s along the same line. When they meet, they grab each other and hang on.

That was so much fun that the boys repeat the collision with the same original velocities, this time moving along parallel lines 1.02 m apart. At closest aproach, they lock arms and start rotating about their common center of mass. Model the boys as particles and their arms as a cord that does not stretch.
Find the belocity of their center. magnitude m/s
direction

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.