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 2.66 km/s at an initial inclination of 48.2 ◦ 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.
This is a case of projectile motion. The given information is:
initial velocity, u = 2.66 km/s = 2660 m/s
inclination, `theta` = 48.2 degrees (to the horizontal)
Acceleration due to gravity, g = 9.8 m/s^2
Maximum horizontal distance traveled or the range of the projectile is given as:
`x = (u^2 sin (2theta))/g`
substituting the values in the equation, we get:
`x = (2660^2 sin(2xx48.2))/(9.8)`
or, x = 717,500 m = 717.5 km
Hope this helps.