Question

A bullet is fired from gun mounted at an angle of 30°. If the muzzle velocity is 400 m/s, calculate:

a. Vertical velocity component

b. Horizontal velocity component

c. Maximum height reach

d. Time of flight

e. Range

Answer 1

Given:

$v_0=400\:\rm m/s$

$g=9.81\:\rm m/s^2$

$\theta=30^{\circ}$

(a) Vertical velocity component

$$v_y=v_0\sin\theta=400*\sin 30^{\circ}=200\:\rm m/s$$

(b) Horizontal velocity component

$$v_x=v_0\cos\theta=400*\cos 30^{\circ}=346\:\rm m/s$$

(c) Maximum height reach

$$h_{\max}=\frac{v_0^2\sin^2\theta}{2g}=\frac{400^2\sin^230^{\circ}}{2*9.81}=2039\:\rm m$$

(d) Time of flight

$$t=\frac{2v_0\sin\theta}{g}=\frac{2*400\sin30^{\circ}}{9.81}=40.8\:\rm s$$

(e) Range

$$h_{\max}=\frac{v_0^2\sin2\theta}{g}=\frac{400^2\sin60^{\circ}}{9.81}=12232\:\rm m$$