The figure shows an overhead view of a ring that can rotate about its center like a merry-go-round. It’s outer edge radius R_2 is 0.6 m, its inner radius R_1 is half of R_2, its mass M is 7.2kg, and mass of crossbars is negligible. It initially rotates at an angular speed of 7.4 rad/s with a cat of mass m=M/4 on its outer edge, at radius R_2. By how much does the cat increase the kinetic energy of the cat-ring system if the cat crawls to the inner edge, at radius R_1?

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.