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...

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.

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gsenviro | College Teacher | (Level 1) Educator Emeritus

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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.

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