f. Relative to Earth, Martha’s spaceship moves at 0.5 c. Suppose halfway on her journey towards Zorg, Martha notices an unidentified spaceship rapidly approaching her from the direction of Zorg. To defend her spaceship, Martha fires a projectile at the unidentified spaceship with speed 0.25 c. What is the speed of the projectile relative to Bob?

Which simple machine is not part of this compound machine? a. lever b. pulley c. inclined plane d. wheel and axle

Name three different units of energy used to measure heat and describe what type of situations each is usually used.

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.