What is the magnitude of the speed of a person standing at the equator due to the rotational speed of mars? (assume a mars day is the same length as an earth day)

11. you want to calculate the displacement of an object thrown over a bridge. using -10 m/s2 for acceleration due to gravity, what would be the total displacement of the object if it took 8 seconds before hitting the water?

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.

Awind turbine is rotating counterclockwise at 0.5 rev/s and slows to a stop in 10 s. its blades are 20 m in length. (a) what is the angular acceleration of the turbine? (b) what is the centripetal acceleration of the tip of the blades at t=0s? (c) what is the magnitude and direction of the total linear acceleration of the tip of the blades at t=0s?