A 2.25 kg pumpkin oscillates from a vertically hanging light spring once every 0.85 s. A) Find the equation giving the pumpkin's position ( upward) as a function of time , assuming it started by being compressed 17 cm from the equilibrium position (where = 0), and released.

y(t)=(.17m) x cos ((2pi)(t))/(.85 s)
B) How long will it take to get to the equilibrium position for the first time? (in s)
C) What will be the pumpkin's maximum speed? (in m/s)
D) What will be its maximum acceleration, and where will that first be attained? (in m/s^2)

Acube has a volume of 2011 cubic inches. what is the angle measure between a side of a cube and its interior diagonal?

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)

Panel bc in fig. p2.76 is semi-circular, with the 3 meter radius and horizontal straight edge through point b. compute (a) the hydrostatic force of the water on the panel, (b) its center of pressure, and (c) the moment of this force about point b. assume atmospheric pressure on the dry side of the panel