How long can Sam expect the possibility of railgun-delivered pizza?
Assume:	Sam accelerates at a = 0.5 m/s2 	maximum railgun velocity of vL = 11.2 kps

High school: I know xf = xi + vi t + ½ a t2
   For Sam: xf = 0 + 0 + ½ (0.5) t2 	For pizza: xf = (11200) t
   When are Sam and the pizza at the same place he can get it, so xsam = xpizza 
   ½ (0.5) t2 = 11200 t   🡺   (0.25) t = 11200   🡺   t = 44800 seconds
   I’ve got a number, I’m done.

College: That’s good, but their relative velocity is a problem – 44,800 seconds after launch, vsam = a t = 22,400 m/s, but the pizza would be moving at 11,200 m/s. Sam would smash into it from behind fast enough to destroy his ship. You want Sam and the pizza at the same place at the same time, but they also have to be moving at the same speed or Sam can’t catch it.
      For Sam:	xsam(t) = ½ a (Δt)2 	;	vsam = a Δt
      For pizza:	xpizza(t) = vL Δt  	;	vpizza = vL 
   For a catch, xsam = xpizza AND vsam = vpizza 
   So…	a Δt = vL   🡺   Δt = vL / a	now plug that in to the other equation…
   ½ a (Δt)2 = vL Δt   🡺   ½ a (vL / a)2 = vL / a   🡺   a (vL2 / a2) = 2 vL / a   🡺   a2 vL2 / a2 = 2 vL 
   vL2 = 2 vL   🡺   vL = 2	  Huh? I wasn’t even looking for that… I wonder if this is on Youtube…

Professor: The railgun could launch before or after Sam, so the start times can be anything we like. The question then becomes when can Sam match speeds with the speeding railgun pizza. Since the pizza is moving at 11.2 kps, and vsam(Δt) = a Δt (ignoring gravity etc.), 22,400 seconds (6h13m20s) after Sam’s launch he’ll be at the same velocity as the pizza (11.2 kps), at a distance of xsam = ½ a Δt2 = 125,440 km from the railgun. To get the pizza there it would have had to have launched 11,200 seconds prior to the rendezvous, or 11,200 seconds after Sam’s launch. The math is left as an exercise for the student, this will be on the exam.

Facebook: x = 0 + 0 t + ½ ½ t2, but the answer is ZERO because anything times zero is zero you guys and you’re stupid common core math…

Engineer: The heat dissipation on the railgun is going to cook your pizza for you while the several hundred G’s it’ll experience on launch is going to pretty much liquify it. But, hey, you spec the job, we’ll build it…

All credit to Freefall Webcomic: http://freefall.purrsia.com/ff3300/fc03247.htm