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 0.725 km/s at
an initial inclination of 73.7◦
to the horizontal.
The acceleration of gravity is 9.8 m/s2

How far away did the shell hit?
Answer in units of km.
How long was it in the air?
Answer in units of s.

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  1. Vi = 725 sin 73.7 = 725*0.96 = 696 m/s upward at start
    m g H = (1/2) m Vi^2
    H = 696^2 / (2 * 9.81) = 48422/(2*9.81) = 24,680 meters max height
    average upward speed = 696/2 = 348 m/s
    so time upward = 24,680/348 = 70.9 seconds upwards
    total time = 2 * 70.9 = 142 seconds
    constant horizontal speed = 725 cos 73.7 = 203.5 m/s
    range = 203.5 * 142 = 28,895 m = 29 kilometers (yikes !)

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