Question

A Marine gunnery sergeant shoots his rifle at the side mirror of a Jeep. Assume that the Jeep is exactly 800 meters away and moving at 30 mph when the trigger is pulled and the mirror is exactly 1.5 meters above the ground. Also, assume that the bullet has sufficient powder to propel the slug the correct distance. What must the initial angle of the rifle be with respect to the horizontal so that the bullet hits the mirror if the muzzle velocity is 725 m/s?

Answer 1

Along the horizontal direction :

v_ox = velocity of the bullet

v_c = velocity of the jeep = 30 mph = 13.41 m/s

d = distance travelled = 800 m

t = time of travel

time of travel is given as

t = d/(v_ox - v_c )

t = 800/(v_ox - 13.41)

Along the vertical direction

h = vertical distance travelled = 1.5 m

using the equation

h = v_oy t + (0.5) a t²

1.5 = (725 Sin) (800/(v_ox - 13.41)) + (0.5) (-9.8) (800/(v_ox - 13.41))²

1.5 = (725 Sin) (800/((725 Cos) - 13.41)) + (0.5) (-9.8) (800/((725 Cos) - 13.41))²

1.5 = (725 sqrt(1 - Cos²)) (800/((725 Cos) - 13.41)) + (0.5) (-9.8) (800/((725 Cos) - 13.41))²

1.5 = (725 sqrt(1 - Cos²?)) (800/((725 Cos) - 13.41)) + (0.5) (-9.8) (800/((725 Cos) - 13.41))²

Cos = 0.99996

= 0.5125 deg