Collision of Projectile Motion

Collision of Projectile Motion is handled by setting the same vertical height and horizontal distance at a given time.

Worked Examples of Collision of Projectile Motion

Two Points $A$ and $B$ are $d$ metres apart. A particle is projected from $A$ towards $B$ with initial velocity $u$ m/s at angle $\alpha$ to the horizontal. Concurrently, another particle is projected from $B$ towards $A$ with initial velocity $w$ m/s at $\beta$ to the horizontal. The particles make a collision of projectile motion when they both reach their maximum height.

The equation of projectile motion projected from the origin with initial velocity $V$ m/s at angle $\theta$ to the horizontal are $x = Vt \cos \theta$ and $\displaystyle y=Vt \sin \theta – \frac{gt^2}{2}$.

(a)    Find the time taken from $A$ to reach its maximum height.

(b)    Show that $u \sin \alpha = w \sin \beta$.

(c)    Show that $\displaystyle d = \frac{uw}{g} \sin(\alpha + \beta)$.