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 1.96 km/s at
an initial inclination of 48.2◦ to the horizontal.
The acceleration of gravity is 9.8 m/s2 .
How far away did the shell hit?
Answer in units of km.
hf=hi+vi*sin48.2*t-4.9t^2
hi,hf =0, solve for t
then, range= viCos48.2*t
change km/s to m/s
To determine how far away the shell hit, we need to calculate the horizontal range covered by the shell.
We can approach this problem using the kinematic equation for horizontal motion:
Range = initial velocity * time
First, we need to find the time it takes for the shell to hit the target. To do that, we can divide the initial velocity in the horizontal direction by the acceleration due to gravity:
time = initial velocity / acceleration due to gravity
Converting the initial velocity from km/s to m/s, we have:
initial velocity = 1.96 km/s * 1000 m/km = 1960 m/s
Substituting the values into the equation:
time = 1960 m/s / 9.8 m/s^2 = 200 seconds
Now, we can calculate the horizontal range covered by the shell:
Range = initial velocity * time
Range = 1960 m/s * 200 s = 392,000 meters
Converting the range from meters to kilometers:
Range = 392,000 m / 1000 m/km = 392 km
Therefore, the shell hit a location approximately 392 km away from its launch point.