A submarine is submerged at a depth of 1213 m. If the atmospheric pressure at the surface is 0.99 bar, the water density is 1000 kg m-3 , and gravity is 9.801 m s-2 , determine:

a) The pressure on the hull of the submarine in [bar] If the volume of the sub is 3×107 ft3 , and the air density inside the sub is 1.23 kg m-3 , determine:
b) The mass of air inside the sub in [kg]
c) The mass of water displaced by the sub in [kg]
d) The buoyancy of the sub in [MN]
Show all calculations, equations, and unit conversions otherwise no points will be given.

Using the given data table, calculate the acceleration of the skateboarder. you can use either form of the equation below?

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

Anybody wanna ? (picture included? )