The image shows the displacement of a motorboat. The data table shows the magnitudes of the components of each displacement vector.

What is the value of Rx?

km

What is the value of Ry?

km

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.

Which process is represented by the pv diagram? a. the isobaric process b. the isovolumetric process c. the isothermal process d. the adiabatic process