Question

During WWI, the Germans had a gun called Big Bertha that was used to shell Paris. The shell had an initial speed of 1700 m/s, and was shot with an inclination of 55 degrees. In order to hit the target, adjustments were made for air resistance. Ignoring frictional effects, calculate the following:

a.The Horizontal and Vertical Velocities

b.How far away did the shell hit?

c. How long was the shell in the air?

Answer 1

Answer:

$975.1\ \text{m/s}$ and $1392.56\ \text{m/s}$

$276830.96\ \text{m}$

284 seconds

Explanation:

(a) $u=\text{Initial velocity}=1700\ \text{m/s}$

$\theta$ = Angle of inclination = $55^{\circ}$

Horizontal velocity is given by

$u_x=u\cos\theta\\\Rightarrow u_x=1700\times \cos55^{\circ}\\\Rightarrow u_x=975.1\ \text{m/s}$

Vertical velocity is given by

$u_y=u\sin\theta\\\Rightarrow u_x=1700\times \sin55^{\circ}\\\Rightarrow u_x=1392.56\ \text{m/s}$

The horizontal and vertical velocities are $975.1\ \text{m/s}$ and $1392.56\ \text{m/s}$ respectively.

(b) Range of projectile is given by

$R=\dfrac{u^2\sin2\theta}{g}\\\Rightarrow R=\dfrac{1700^2\sin(2\times 55^{\circ})}{9.81}\\\Rightarrow R=276830.96\ \text{m}$

The shell hit the ground $276830.96\ \text{m}$ from the launch position.

(c) Time of flight is given by

$t=\dfrac{2u\sin\theta}{g}\\\Rightarrow t=\dfrac{2\times 1700\times \sin55^{\circ}}{9.81}\\\Rightarrow t=284\ \text{s}$

The shell was in the air for 284 seconds.