4. The diagram represents the path of a ball that has been thrown upward. Discuss how the kinetic energy (KE), gravitational potential energy (GPE), and total mechanical energy (ME) change between points A (where the ball is thrown from), B (the highest point reached by the ball), and C (where the ball hits the ground). Ignore friction between the ball and the air. (3 points) B A C

After the near spacecraft passed mathilde, on several occasions rocket propellant was expelled to adjust the spacecraft's momentum in order to follow a path that would approach the asteroid eros, the final destination for the mission. after getting close to eros, further small adjustments made the momentum just right to give a circular orbit of radius 45 km (45 × 10^3 m) around the asteroid. so much propellant had been used that the final mass of the spacecraft while in circular orbit around eros was only 545 kg. the spacecraft took 1.04 days to make one complete circular orbit around eros. calculate what the mass of eros must be.

The pressure, volume, and temperature of a mole of an ideal gas are related by the equation pv = 8.31t, where p is measured in kilopascals, v in liters, and t in kelvins. use differentials to find the approximate change in the pressure if the volume increases from 14 l to 14.6 l and the temperature decreases from 375 k to 370 k. (round the answer to two decimal places.)

Amodel rocket with a mass of 0.212 kg is launched into the air with an initial speed of 84 m/s. how much kinetic energy will the rocket have at a height of 214 m? assume there is no wind resistance. 634 j 303 j