A satellite is placed into orbit around the planet Kaitain. The desired orbit has a radius of 2.3×106 m, and Kaitain has a mass of 4.31×1025kg. a) How much gravitational field is there at this orbital radius?
b) What velocity does this satellite need to orbit with?
c) What will this satellite’s orbital period be?

Emmy kicks a soccer ball up at an angle of 45° over a level field. she watches the ball's trajectory and notices that it lands, two seconds after being kicked, about 20 m away to the north. assume that air resistance is negligible, and plot the horizontal and vertical components of the ball's velocity as a function of time. consider only the time that the ball is in the air, after being kicked but before landing. take "north" and "up" as the positive ‑ and ‑directions, respectively, and use ≈10 m/s2 for the downward acceleration due to gravity.

Four identical lab carts each have a mass of 200 kg. different masses are added to the carts and the velocities are measured. all carts move to the right.

The illuminance of a surface varies inversely with the square of its distance from the light source. if the illuminance of a surface is 120 lumens per square meter when its distance from a certain light source is 6 meters, by how many meters should the distance of the surface from the source be increased to reduce its illuminance to 30 lumens per square meter?