Question

What is the average velocity of a particle projected from the ground with speed u at an angle alpha with horizontal over a time interval from beginning till it strikes the ground again?

Answer 1

The average velocity of a particle projected from the ground with speed u at an angle alpha with horizontal over a time interval from beginning till it strikes the ground again is Ucos$\alpha$

• We know the average velocity is defined as total displacement/ total time

• That means Average velocity  =  total displacement / total time

• In a projectile motion, the total displacement of the projectile is the Range of the particle.

• Since displacement is the shortest distance between beginning and end points, net displacement  = Range
• Now total time taken = Time of flight = Tf
• We know Range = horizontal component of velocity x time of flight
• Therefore Average velocity = Range/Time of flight

• Vav  = horizontal component of velocity x time of flight/Time of flight

• Vav = horizontal component of velocity = Ucos$\alpha$

Therefore average velocity  = Ucos$\alpha$