Find the magnitude of the resultant force and the angle it makes with the positive x-axis. (let a = 30 lb and b = 18 lb. round your answers to one decimal place.)

State one advantage and one disadvantage of using a plane mirrior as a driving mirrior

There is a theory that indicates that dinosaurs became extinct when about 65 million years ago, a large asteroid hit the earth surface. dust caused by this collision blocked the sunlight reaching the earth's surface and many forms of life became extinct due to the cold. fearing this threat, how large the radius of an asteroid should you be looking for if the dangerous asteroid size is approximately the same as the one that killed the dinosaurs? available data suggests that about 18% of that asteroid's mass ended up as a dust spread evenly over earth after eventually settling out of the upper atmosphere. about 0.0180 g/cm^2 of dust, which is chemically different than the earth's rock, covered the earth's surface. typical asteroids have a density of about 1.9 g/cm^3. now that we know the size of the asteroid, how much energy was released during impact, assuming all of it was just the kinetic energy of the asteroid right before the impact?

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.