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