A lunar lander is making its descent to Moon Base I. The lander descends slowly under the retro-thrust of its descent engine. The engine is cut off when the lander is h - 5.0 m above the surface and has a downward speed of 0.7 m/s. With the engine off, the lander is in free fall. What is the speed of the lander just before it touches the surface? The acceleration due to gravity on the moon is 1.6m/s^2.

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.

On a geologic map, if the contacts between sedimentary rock units form a bull’s-eye pattern of concentric circles, with the youngest unit in the center, the underlying structure is a(n)

The frequency of the fundamental of the guitar string is 320 hz. at what speed v do waves move along that string?