An astronaut with a mass of 91 kg is 0.30 m above the moons surface. The astronauts potential energy is 46 J. Calculate the free-fall acceleration on the moon?

Alarge truck is moving 22.0 m/s. if it’s momentum is 125,000 kg • m/s, what is the trucks mass

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.

Two 2.0-cm-diameter disks face each other, 1.0 mm apart. they are charged to ±10 nc. what is the electric field strength between the disks? a proton is shot from the negative disk toward the positive disk. what launch speed must the proton have to just barely reach the positive disk?