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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 2.07 km/s at an initial inclination of 28.8 ◦ 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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luchoprat

Answer:

d = 369.38 km

Explanation:

The speed has a x-component and a y-component.

speed,x = 2.07cos(28.8°) = 1.81 km/s

speed,y = 2.07sin(28.8°) = 1.00 km/s

The time the shell flies is determined by the y-component, when it reaches the highest point the speed is 0 due to the gravitational acceleration.

[tex]v_{f}=v_{0} +a * t[/tex]

0 = 1000 - 9.8 * t

9.8 * t = 1000

t = 102.04 s

After reaching the highest point the shell takes the same time to reach the ground where it was fired, so the total time it flies is 102.04* 2 = 204.08 s

Now you can calculate the distance it moves horizontally while it flies (constant speed)

[tex]d = v*t[/tex]

d = 1.81 km/s * 204.08 s (I used the speed in km/s because the answer needs to be in km)

d = 369.38 km

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