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

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

`276830.96\ \text{m}`

284 seconds

Step-by-step 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* \cos55^(\circ)\\\Rightarrow u_x=975.1\ \text{m/s}`

Vertical velocity is given by

`u_y=u\sin\theta\\\Rightarrow u_x=1700* \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=(u^2\sin2\theta)/(g)\\\Rightarrow R=(1700^2\sin(2* 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=(2u\sin\theta)/(g)\\\Rightarrow t=(2* 1700* \sin55^(\circ))/(9.81)\\\Rightarrow t=284\ \text{s}`

The shell was in the air for 284 seconds.