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.

think its the third option