A0.180-kg cube of ice (frozen water) is floating in glycerine. the gylcerine is in a tall cylinder that has inside radius 3.50 cm. the level of the glycerine is well below the top of the cylinder. if the ice completely melts, by what distance does the height of liquid in the cylinder change? does the level of liquid rise or fall? that is, is the surface of the water above or below the original level of the glycerine before the ice melted?

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.