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 1.86 km/s at an initial inclination of 52.2◦ to the horizontal. The acceleration of gravity is 9.8 m/s^2.
a. How far away did the shell hit? Answer in units of km.
b. How long was it in the air? Answer in units of s.
you know that
(a) R = v^2/9.8 sin2θ
(b) h(t) = v*sinθ - 4.9t^2
solve for h=0
To determine how far away the shell hit (part a), we need to calculate the horizontal distance traveled by the shell.
To do this, we can break down the initial velocity of the shell into its horizontal and vertical components. The horizontal component of the velocity remains constant throughout the shell's flight, while the vertical component is affected by gravity.
Given:
Initial velocity (v₀) = 1.86 km/s
Initial inclination (θ) = 52.2°
Acceleration due to gravity (g) = 9.8 m/s²
First, we need to convert the initial velocity to m/s:
1.86 km/s = 1860 m/s
Next, we can find the horizontal component of the velocity:
v₀x = v₀ * cos(θ)
Substituting the values:
v₀x = 1860 * cos(52.2°)
Now, we can calculate the time of flight (part b) using the equation:
t = 2 * v₀y / g
Where v₀y is the vertical component of the initial velocity and is given by:
v₀y = v₀ * sin(θ)
Now, let's calculate the horizontal distance (part a) using the equation:
d = v₀x * t
We can plug in the values we calculated to find the distance and time in the air:
a. Distance (d):
d = v₀x * t
b. Time (t):
t = 2 * v₀y / g
Let's calculate the values:
Horizontal Component of Velocity (v₀x):
v₀x = 1860 * cos(52.2°)
Vertical Component of Velocity (v₀y):
v₀y = 1860 * sin(52.2°)
Time of Flight (t):
t = 2 * v₀y / g
Distance (d):
d = v₀x * t
To calculate these values, I need to know the specific values of the initial velocity, inclination angle, and acceleration due to gravity. Please provide those values.