A water balloon is observed to emerge from an open window of a gymnasium. The window is 9.5 m above the ground. Through miracles of technology (involving doppler radar and automated video analysis), it is determined that the balloon leaves the window with a speed of 12.5 m/s at an angle of 45∘
45
∘
relative to horizontal.
(A) How much time elapses from when the balloon is passing through the window to when it hits the ground? s
(B) How far from the wall does the balloon hit the ground? m

It is determined that someone within the gymnasium threw the balloon from the floor level of the gymnasium, which is level with the ground outside.
(C) Assuming the launch point is from the floor level, how far from the wall was the balloon launched? m

Industrial processes often require the damping of vibrations. consider a workbench that uses four large ideal springs in place of traditional legs, with each spring supporting one corner of the workbench and exhibiting a force constant of 47500 n/m. this workbench is used when creating products that involve highly unstable chemicals. according to specifications, the acceleration of the manufacturing equipment must be held to less than 22.3 m/s2 for the manufacturing process to proceed safely. the amplitude of vibrations are expected to remain under 0.622 mm throughout. given that the workbench and maufacturing equipment combine to 6.05 kg, find the maximum acceleration expected of the equipment and workbench. (ignore the mass of the springs.)