## Collisions in Mid Air

Particles will collide if they are in the same place at the same time. Particles that collide in mid air, subject only to the force of gravity will be moving as projectiles, and the simplest typ of collision that can take place is between particles moving vertically.

Suppose then that one particle is thrown up from the ground with a speed of 10 m/s and simultaneously another particle is dropped from a point 8 m vertically above the first one. Applying SUVAT to each particle in the direction of motion of each particle.

 Particle 1 Particle 2 s ? s ? u 10 u 0 v ? v ? a -9.8 a 9.8 t ? t ?

There are also two conditions we can use. Sine the particles start moving at the same time, t is the same for both, and when the particle collide, they will have moved a total of 8 m so that when the particles collide, if particle 1 has moved a distance y, particle 2 will have moved a distance 8-y. The table becomes

 Particle 1 Particle 2 s y s 8-y u 10 u 0 v ? v ? a -9.8 a 9.8 t t t t

For particle 1, using gives For particle 2, using gives Adding these two equations gives and this collision point is independent of the acceleration due to gravity.

In fact the particles are at each moment of the motion moving together with combined speed 10. If the initial combined approach speed of both particles is and the distance between them is then they will collide after a time  