You are in an egg drop contest which you win by breaking your egg the hardest. you drop your egg off of a 3 story building (12m above the ground). you can throw it up with speed 11m/s, or straight down with speed 11m/s. write a way to break it.

Ok, first start writing our movement equation.

First our acceleration will be the gravity; so a= g

integrating we can obtain the velocity  v= g*t + v₀

where v₀ depends on if we trhow the egg upsides or downsides, being the positive direction downsides.

after, the position will be r = +  v₀*t - 12m

where the -12m is because you are upside a building.

first case: straight down with speed 11m/s

so the velocity is positive

then, if we  do +  11*t - 12m = 0 and with bashkara obtain the positive root for the time t=1.6 seconds

putting this on our velocity equation you will get v = 10*1.6 + 11 = 27m/s is the velocity of the egg when it hits the ground.

for the other case, our equation will have the form of:

  -  11*t - 12m = 0

and the positive root of the time is: t = 3 seconds.

putting it in the velocity equation gives you v= 10*3 - 11 = 29m/s

which is bigger than the first case, so the egg hits the ground with more velocity, ence more energy.

the working equation for the angular size is the product of the physical size and 360 degrees divided by the product of two pi and distance from earth. the minimum size would be 0.559 degrees while the maximum size would be 0.49 degrees.