During an off-day, mike trout, shohei ohtani, and albert pujols and having a pool party. they are tugging on a ring for some odd reason (the angels are weird…). trout pulls with a force of 150 n directly north, ohtani pulls directly east with a force of 100 n, and pujols pulls southwest (225° clockwise from north) with a force of 200 n. what is the resultant force and what is the direction of the resultant force?

Aquantity of gas has a volume of 1.5 m3 and an absolute pressure of 95 kpa. when the gas is compressed to a volume of 0.5 m3, what is the new absolute pressure of the gas? (assume that there’s no change in temperature.)

Astate of matter all that has define volume and can flow is a(n)

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.