Prove the correctness of this equation s=vt + 1/2at ​

Comedians like to joke that the reason we haven’t been visited by intelligent life from elsewhere in the universe is that aliens have been monitoring earth’s broadcasts of intellectually embarrassing tv programs, like gilligan’s island, fear factor, the jersey shore, and the jerry springer showand so consider us far too primitive to merit a visit. let’s check the assertion that aliens could have been receiving them. tv programs are broadcast at a frequency of about 100mhz with about 100kw of total power in 30frames per second, which emanatesroughly uniformly in all directions. assume that interstellar space transmits these broadcasts without attenuation. no matter how smart they are, aliens would require at least one photon per frame to interpret our signals. findthe number of photons per unit time per unit area reaching a receiver on a possible planet in the nearest star system, which is about 4 light-years away (a light-year is the distance light travels in a year). if aliens aimed a receiver or detector directly at earth, how big (in diameter) would it have to be to receive a photon per frame

When you push downward on a book at rest on a table, you feel an upward force. does this force depend on friction? defend your answer.

At a certain instant after jumping from the airplane a, a skydiver b is in the position shown and has reached a terminal (constant) speed vb = 52 m/s. the airplane has the same constant speed va = 52 m/s, and after a period of level flight is just beginning to follow the circular path shown of radius ρa = 2330 m. (a) determine the velocity and acceleration of the airplane relative to the skydiver. (b) determine the time rate of change of the speed vr of the airplane and the radius of curvature ρr of its path, both as observed by the nonrotating skydiver.