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?
Answer in units of km

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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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