At a picnic, there is a contest in which hoses are used to shoot water at a beach ball from three directions. as a result, three forces act on the ball, upper f subscript 1 baseline overscript right-arrow endscripts, upper f subscript 2 baseline overscript right-arrow endscripts, and upper f subscript 3 baseline overscript right-arrow endscripts (see the drawing). the magnitudes of upper f subscript 1 baseline overscript right-arrow endscripts and upper f subscript 2 baseline overscript right-arrow endscripts are f1 = 26.0 newtons (n) and f2 = 54.0 n. determine (a) the magnitude of upper f subscript 3 baseline overscript right-arrow endscripts and (b) the angle θ such that the resultant force acting on the ball is zero.

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