# physics

During World War I, the Germans had a gun
called Big Bertha that was used to shell Paris.
The shell had an initial speed of 2.39 km/s at
an initial inclination of 49.6

to the horizontal.
The acceleration of gravity is 9.8 m/s
2
.
How far away did the shell hit?

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1. vertical problem
Vi = 2390 sin 49.6

v = Vi - 9.8 t
at top v = 0
so
t = Vi/9.8 at top
that is half the trip
hits ground at tg = Vi/4.9

Now the horizontal problem
u = 2390 sin 49.6
range = u tg
range = 2390 sin 49.6 * Vi/4.9
so
range = 2390^2 sin 49.6 cos49.6 /4.9
= 575369 meters
= 575 km

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