Answer to Question #305193 in Classical Mechanics for mosaddek

Question

A projectile is fired at an angle 30 ° from gun that is 45 m above the flat ground, emerging from the gun with a speed of 250 m/s. (a) How long does the projectile remain in air? (b) At what horizontal distance from the firing ground does it strike the ground? (c) What is the velocity of the projectile when it hits the ground?

Answer 1

Given:

$\theta=30^\circ$

$y_0=45\:\rm m$

$v_0=250\:\rm m/s$

$g=9.8\:\rm m/s^2$

(a)

$$y=y_0+v_0\sin\theta t-gt^2/2=0$$

$$45+125 t-4.9t^2=0$$

$$t=26\:\rm s$$

(b)

$$x=v_0\cos\theta t\\ =250*\sqrt{3}/2*26=5630\:\rm m$$

(c)

$$v=\sqrt{v_0^2+2gy_0}\\ =\sqrt{250^2+2*9.8*45}=252\:\rm m/s$$