About once every 30 minutes, a geyser known as old faceful projects water 18.0 m straight up into the air. use g = 9.80 m/s2, and take atmospheric pressure to be 101.3 kpa. the density of water is 1000 kg/m3. what is the speed of the water when it emerges from the ground?

When you drop a pebble from height a it reaches the ground with speed v if there is no air resistance. from what height should you drop it so it will reach the ground with three times the speed? (a) 9m (b) 3m (c) 6m (d) 18m

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.

The image below shows numerous volcanic mountains in the pacific northwest. what is the most likely cause of the volcanic and earthquake activity in this region?