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 1.4 km/s at an initial inclination of 65.8 ◦ to the horizontal. The acceleration of gravity is 9.8 m/s 2. How far away did the shell hit?

The shell hit at a horizontal distance 149.41 km

Explanation:

The shell had an initial speed of 1.4 km/s

Initial speed = 1400 m/s

Inclination = 65.8° to the horizontal

First let us find the time of travel

Consider the vertical motion,

We have equation of motion, s = ut + 0.5 at²

Initial velocity, u = 1400 sin 65.8 = 1276.97 m/s

Acceleration, a = - 9.81 m/s²

Displacement, s = 0 m

Substituting

s = ut + 0.5 at²

0 = 1276.97 x t + 0.5 x (-9.81) xt²

t = 260.34 s

Now let us find the horizontal displacement,

Consider the horizontal motion,

We have equation of motion, s = ut + 0.5 at²

Initial velocity, u = 1400 cos 65.8 = 573.89 m/s

Acceleration, a = 0 m/s²

Time, t = 260.34 s

Substituting

s = ut + 0.5 at²

s = 573.89 x 260.34 + 0.5 x 0 x 260.34²

s = 149407.11 m = 149.41 km

The shell hit at a horizontal distance 149.41 km