Physics Projectile Motion

Question

An artillery shell is fired at an angle of 46◦ above the horizontal ground with an initial speed of 1620 m/s. The acceleration of gravity is 9.8 m/s 2 . (a)Find the total time of flight of the shell, neglecting air resistance. Answer in units of min.

(b)Find its horizontal range, neglecting air resistance. Answer in units of km

Answer 1

(a) We have equations of motion: x = 1620cos46°t, y = 1620sin46°t - 4.9t².

At final moment y = 0 and 1620tsin46°t - 4.9t² = 0, t = 0 (moment of fired) or t = 1620sin46°/4.9 = 237.8 s = 3.964 min

(b) Horizontal distance x = 1620cos46°·237.8 m = 267607.4 m = 267.6 km