During World War I, the Germans had a gun called Big Bertha that was used to shell Paris.

Question

The shell had an initial speed of 2.12 km/s at an initial inclination of 78.7 ◦ to the horizontal. The acceleration of gravity is 9.8 m/s 2 .

-How far away did the shell hit?

-How long was it in the air?

Answer 1

Hi Elizabeth,

This is a kinematics problem, specifically free fall in 2D. First we need to evaluate what is given, and the unknowns. Defining the initial point as the launch point and the final point as the impact:

Also, remember that the kinematic equations can be used in x or y, one at a time. No component values are allowed, including the given speed. All values need to be in SI units.

vix = vi*cos(theta)

viy = vi*sin(theta)

yi = 0

yf = 0

xi = 0

xf = ? <-- part a

ay=-9.8 (the negative because it pulls downwards)

ax=0

t = ? <-- part b

vfx = vix (ax=0 means constant velocity)

vfy = ?

time is easier to find first:

b) since we don't know vfy, use

yf = yi + viy*t + 0.5*ay*t^2

0 = 0 + vi*sin(theta)*t - 0.5g*t^2

t = vi*sin(theta) / (0.5*g) = 2120*sin(78.7) / (0.5*9.8) = 424.8 s

b) range equation:

xf = xi + vix*t

xf = 0 + vi*cos(theta)*t

= 2120*cos(78.7)*424.8=174524 m

= 174 km

a picture would be much easier here, please contact me and I can send you a drawing of the problem.