A bobsled zips down an ice track starting at 150 m vertical distance up the hill. Disregarding friction, what is the velocity of the bobsled at the bottom of the hill? (g = 9.81 m/s2

Agas initially at p1 = 1 bar and occupying a volume of 0.5 liter is compressed within a piston–cylinder assembly to a final pressure p2 = 4 bar. (a) if the relationship between pressure and volume during the compression is pv = constant, determine the volume, in liters, at a pressure of 3 bar. (b) repeat for a linear pressure–volume relationship between the same end states. reference

Standing side by side ,you and a friend step off a bridge at different times and fall for 1.6s to the water below. your friend goes first, and you follow after he has dropped a distance of 2.0m. when your friend hits the water, is the seperation between the two of you 2.0m or more than 2.0m? verify your answer with a calculation.

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k