In a science fiction story, a microscopic black hole is given an enormous positive charge by firing an un-neutralized ion drive exhaust (consisting of positively charged xenon ions) into it for six months. The idea behind the charging process is to be able to confine and manipulate this dangerous object with powerful electric fields. Suppose the charge on the black hole is 5740 C. At what distance from it is the electric potential equal to 1.09e 3 V

Cathy is pedaling down a steep hill on her bicycle and wants to be able to coast up the next hill, which is 25 meters high, without pedaling. cathy and her bicycle have a mass of 75 kg. assuming her bicycle is 100% efficient, what would her speed have to be?

Asilver dollar is dropped from the top of a building that is 1324 feet tall. use the position function below for free-falling objects. s(t) = −16t2 + v0t + s0 (a) determine the position and velocity functions for the coin. s(t) = v(t) = (b) determine the average velocity on the interval [1, 2]. ft/s (c) find the instantaneous velocities when t = 1 second and t = 2 seconds. v(1) = ft/s v(2) = ft/s (d) find the time required for the coin to reach the ground level. (round your answer to three decimal places.) t = s (e) find the velocity of the coin at impact. (round your answer to three decimal places.) ft/s

What is the role of the water cycle in maintaining freshwater levels in lake and rivers?