a 40kg surfer jumps off the back of a 20kg surfboard moving forward. find the surfboards velocity immediately after the girl jumps, assuming the surfboards initial velocity is 8 m/s and the girls velocity when jumping off the board is 3 m/s

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.)

Asheet of steel 1.5 mm thick has nitrogen atmospheres on both sides at 1200oc and is permitted to achieve a steady-state diffusion condition. the diffusion coefficient for nitrogen in steel at this temperature is 6 x 10- 11 m2 /s, and the diffusion flux is found to be 1.2 x 10-7 kg/m2 -s. also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 4 kg/m3 . how far into the sheet from this high-pressure side will the concentration be 2.0 kg/m3 ? assume a linear concentration profile.

It is reasonable to assume that the bulk modulus of blood is about the same as that of water (2.2 gpa). as one goes deeper and deeper in the ocean, the pressure increases by 10000 pa for every meter below the surface. if a diver goes down 80.0 m in the ocean, by how much does each cubic centimeter of her blood change in volume? give the answer in cubic centimeters (actually one cubic centimeter equals one milliliter).