I'm stuck on this question. show all work!
an airplane undergoes the following displacements: first, it flies 72 km in a direction 30° east of north. next, it flies 48 km due south. finally, it flies 100 km 30° north of west. using analytical methods, determine how far the airplane ends up from its starting point.

A23 kg log of wood begins from rest, 300 m up a sluice (a water track used to transport logs, think of it as an inclined plane with negligible friction) inclined at 20° to the horizontal. after it reaches the flat waterway at the bottom it collides elastically with a 100 kg block of wood initially at rest near the base of the incline. (a) how long does it take the 23 kg log to travel down the incline? (b) what is the speed of the 23 kg log at the bottom of the incline? (c) what are the velocities of both blocks of wood after the collision? (d) what is the total kinetic energy before the collision? (e) what is the kinetic energy of the 23 kg log after the collision? (f) what is the kinetic energy of the 100 kg block of wood after the collision? (g) what is the total kinetic energy after the collision? (h) compare the total initial and total final kinetic energies. is this consistent with what you would expect for elastic collisions? explain!

The diagram shows a series of volcanic island and a hot spot determine the direction of movement of the tectonic plate that for the island

A5 foot by 5 foot box culvert is buried 6 feet beneath the surface of the ground. a crosssection of this very long culvert (into and out of the page) is illustrated below. assume that the soil in which the culvert is buried has the following properties: jt = 120 pcf, w = 12%, ko = 0.50, ka = 0.33, and kp = 3.00. calculate the total horizontal force per unit length of culvert (fh) felt on one of the vertical faces of the culvert.