An attacker at the base of a castle wall 3.65 m high throws a rock straight up with speed 7.4m/s from a height of 1.55m above the ground.

a) will the rock reach the top?
b) if so what is its speed at the top? if not, what initial speed must it have to reach the top?
c) find the change in speed of a rock thrown straight down from the top of the wall at an initial speed of 7.4 m/s and moving between the same two points.
d) does the change in speed of the downward moving rock agree with the magnitude of the speed change of the rock moving upward between the same elevations?
e) why does this agree or not agree.

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)

Steelhead trout migrate up stream to spawn.occasionally they need to leap up small waterfalls to continue their journey. fortunately, steelhead are remarkable jumpers, capable of leaving the water at a speed of 8.0 m/s. a. what is the maximum height a steelhead trout can jump? b.leaving the water at 8.0 m/s, the trout lands on top of the water fall 1.8 m high. how long was it in the air?

You add 800 ml of water at 20c to 800 ml of water at 80c what is the most likely final temperature of the mixture ? a. 100c b. 60c c. 25 c d.50c