Are the days with the longest daylight always in the summer? Are the days with the shortest daylight always in the winter? explain.

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.

Use the profile illustrated for problem (1). assume that the layer of silty sand fill (sm) is placed over the entire site. estimate the thickness of the fill (h - in feet) that will cause the effective vertical stress at the center of the clay layer to increase by 517.5 pounds per square foot.

Atriangle with equal sides of length 10 cm has -2.5-nc charged objects at each corner. part a determine the direction of the electrical force exerted on the object at the top corner due to the two objects at the horizontal base of the triangle. determine the direction of the electrical force exerted on the object at the top corner due to the two objects at the horizontal base of the triangle. horizontally rightward vertically downward vertically upward horizontally leftward