For the following questions consider the diagram respresentimg a potion of an amusement park ride assume a 100kg car has 30,000 or potential energy at point a it moves down a frictionless track and comes to a stop as it compresses a huge spring at point D. Calculate how much kinetic energy the car has at point c.
How fast is the car moving? show work

The number of passengers who arrive at the platform of a subway station for the 10 am train is a random variable with a mean of 120 and a variance of 16. find the lower bound of the probability that there will be between 100 and 140 passengers (round off to second decimal place).

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

Aflask with vinegar in it has a mass of 160 grams. a balloon with baking soda in it has a mass of 40 grams. the balloon is attached to the flask to seal the opening and the vinegar and baking soda mixes. the balloon inflates to a large volume. what will the total mass of the balloon and flask be after the balloon inflates? explain. a) less than 200 grams because the solid baking soda disappears. b) 200 grams, because all the atoms remain in the balloon or flask. c) more than 200 grams because the size of the balloon is so much larger. d) less than 200 grams because gases such as the one in the balloon are lighter than solids and liquids.