Suppose that the mars orbiter was to have established orbit at 155 km and that one group of engineers specified this distance as 1.55 × 105 m. suppose further that a second group of engineers programmed the orbiter to go to 1.55 × 105 ft. what was the difference in kilometers between the two altitudes? how low did the probe go?

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.

Suppose you increase your walking speed from 7 m/s to 13 m/s in a period of 2 s. what is your acceleration?

1. jay fills a wagon with sand (about 20 kg) and pulls it with a rope 30 m along the beach. he holds the rope 25° above the horizontal. the rope exerts a 20-n tension force on the wagon. how much work does the rope do on the wagon?