The first modern liquid fuel rockets were developed about a century ago. These were ballistic rockets, meaning

that the majority of the flight path was that of a projectile, with just a small portion of the path under propulsion.

From Wikipedia, we can get some information about one of the most successful versions of these rockets, the

German V$2.$ The numbers that I care the most about are maximum height $($Hmax $=206$km$)$ to which the

rocket will rise if launched vertically, the maximum height $($hmax $=88$km$)$ it will rise if launched at an angle

to maximize the range $($Rmax $=320$km$),$ and finally the maximum speed $($vmax $=5,760$km$/$hr$).$ Our goal is to

assess these numbers in the context of the formulas we have from class.

$($a$)$ For an ideal projectile, what is Rmax$/$Hmax$?$ How does this compare to the numbers for the V$2$ rocket?

$($b$)$ For an ideal projectile, what is Rmax$/$hmax$?$ How does this compare to the numbers for the V$2$ rocket?

$($c$)$ What would be the magnitude of the initial velocity for an ideal projectile with a maximum range of

Rmax $=320$km$?$ How does this compare to the numbers for the V$2$ rocket?

$($d$)$ The average acceleration of the V$2$ rocket was a $=25$m$/$s

$2$ when the engine was operating. Estimate the

amount of time that the engine operated.