A skateboarder is trying to skate horizontally off a building and jump over a pool as shown! The pool is 20.0m wide and the roof of the building is 27.0m above where he will land. Neglect drag. How long will the skateboarder remain in the air?

With what initial speed (in given units) does the skateboarder need to barely clear the pool?

Would the skateboarder clear the pool if he skated off the building with an initial speed of 15mph?

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.

Agraduated cylinder contains 63.0 ml of water. a piece of gold, which has a density of 19.3 g/ cm3, is added to the water and the volume goes up to 64.5 ml. calculate the mass in grams of the gold that was added to the water. explain how you got your answer.

The voltage applied across a given parallel-plate capacitor is doubled. how is the energy stored in the capacitor affected?