Projectile Motion

Question

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 1.75 km/s at an initial inclination of 27◦ to the horizontal. The acceleration of gravity is 9.8 m/s 2 . How far away did the shell hit? Answer in units of km. How long was it in the air? Answer in units of s.

Answer 1

Vertical: (free fall, how long in the air)

t = ?

v_yi = 1.75sin27 = 0.794 km/s = 794 m/s

v_yf = -794 m/s (with no air resistance there is symmetry in free fall)

a_y = -9.8 m/s/s

t = (v_f - v_i)/a

t = (-794-794)/-9.8

t = 162 seconds

Horizontal: (constant velocity, use time in air from vertical motion)

d_x = ?

v_x = 1.75cos27 = 1.559 km/s = 1,559 m/s

t = 162 s

d = v*t

d = 1559*162

d = 252,600 m = 252.6 km