Bill kicks a rock off the top of his apartment building. It strikes a window across the street 11 m away. The acceleration of gravity is 9.8 m/s 2 . If the window is 16 m below the position where Bill contacted the rock, How fast was it moving when it left Bill’s foot?

During physical science, ms. greene challenged her students to produce an energy transformation. james and jill wrapped a 4-inch nail with a coil of fifty turns of wire. they connected one end of the coil to one terminal of a knife switch. they connected the other terminal of the knife switch to the battery. finally, they connected the end of the coil to the other terminal of the battery. james held the tip of a 1-inch nail near the flat end of the 4-inch nail. jill closed the knife switch quickly and then opened it. the 1-inch nail was pulled toward the 4-inch nail. what is the best explanation of why the nail moved? a) electrical energy was converted to mechanical energy in the 1-inch nail. b) the 4-inch nail became an electromagnet and the magnetic force attracted the 1-inch nail. c) the electric current in the 4-inch nail was converted to mechanical energy in the 1-inch nail. d) the 4-inch nail had a positive charge and the 1-inch nail had a negative charge. opposites attracted.

Astudent wears sunglasses to her read a book more easily which wave interaction occurs as light passes from the air into the plastic lenses? a polarization b.refraction c.diffraction d. interference

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