A stone is thrown from a rooftop at time t=0 seconds. Its position at time t is given by r⃗ (t)=8ti−3tj+(24.5−4.9t^2)k. The origin is at the base of the building, which is standing on flat ground. Distance is measured in meters. The vector i points east, j points north, and k points up.

a) How high is the rooftop?

(b) When does the stone hit the ground?

(c) Where does the stone hit the ground? (in meters)

(d) How fast is the stone moving when it hits the ground?

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

Which fact supports the conclusion that there will be fewer farm managers in the future? a) a farmer manager’s duties vary by the type of farm. b) farm technology is replacing some administrative jobs c) farm managers often need experience but not education. d) administrative duties include budgeting and training staff.

Adiver named jacques observes a bubble of air rising from the bottom of a lake (where the absolute pressure is 3.50 atm) to the surface (where the pressure is 1.00 atm). the temperature at the bottom is 4.00 ∘c, and the temperature at the surface is 23.0 ∘c.what is the ratio of the volume of the bubble as it reaches the surface (vs) to its volume at the bottom (vb)? if jaques were to hold his breath the air in his lungs would be kept at a constant temperature. would it be safe for jacques to hold his breath while ascending from the bottom of the lake to the surface?