Alien scientists discover an asteroid headed directly towards their planet. The alien planet has a mass of M=6.39x1023 kg and the asteroid has a mass of m=1.50x108 kg. When the asteroid is a distance r1=3.40x108 m from the center of the alien planet, it has a velocity v1=1.00 m/s. The alien scientists calculate it will hit the surface of the planet with velocity v0=4982.00 m/s. What is the radius of the alien planet?

An insulated 40 ft^3 rigid tank contains air at 50 psia and 120°f. a valve connected to the tank is now opened, and air is allowed to escape until the pressure inside drops to 25 psia. the air temperature during this process is kept constant by an electric resistance heater placed in the tank. determine the electrical work done during this process.

Imagine an isolated positive point charge q (many times larger than the charge on a single proton). there is a charged particle a (whose charge is much smaller than charge q) at a distance from the point charge q. on which of the following quantities does the magnitude of the electric field created by charge q at particle a's position depend? check all that apply.the type of the charge on the charged particle athe relative orientation between q and a (while the distance between q and a is fixed)the specific location of the charged particle a (while the distance between q and a is fixed)the amount of the charge on the point charge qthe specific location of the point charge q (while the distance between q and a is fixed)the distance between the point charge q and the charged particle athe amount of the charge on the charged particle a

You are the coordinator for a program that is going to take place at night in a rectangular amphitheater in the mountains. you will have no access to any electricity, but you must be able to illuminate the entire grounds. you know the intensity of the light from a lantern varies inversely as the square of the distance from the lantern. suppose the intensity is 90 when the distance is 5 m. a. write an equation to model the situation. b. solve for the constant of variation. c. write the equation to model the situation using the constant () of variation. d. you have been given lanterns with 40 light intensity. use your equation to solve for the distance from the lantern. e. you need to illuminate 225 km. how many meters do you need to light? f. how many lanterns will you need?