An object of mass m is held at rest a distance Re above the earth’s north pole, where Re is the radius of the earth and g is the accelera- tion due to gravity on the surface. If the object is allowed to fall, with what speed does it hit the surface? Ignore the mo- tion of the earth around the sun, and friction with the earth’s atmosphere.

This energy transformation diagram represents the energy of a skateboarder moving along a half-pipe. as she skates toward the top of the half-pipe, her original kinetic energy is converted to potential energy and friction. how much of the energy is potential?

Why is rain likely when warm, moisture-laden air meets cold air? a) the lighter warm air will rise and cool down, causing condensation and rain. b) the cold air moves faster and pushes the warm air away, causing condensation and rain. c) the moisture in the warm air condenses on contact with the cold air, causing rain to fall. d) the cold air mixes with the warm air, reducing its temperature causing moisture to condense.

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).