Question

derivation of initial velocity equal to final velocity in a projectile

Answer 1

V is velocity of projectile

Horizontal component is Vx=Vcos θ

If we neglect air resistance that final velocity in horizontal direction will be equal to initial velocity in horizontal direction i.e is Vx=Vcos θ

When there is no resistance in horizontal direction then acceleration will be zero.

Using v=u+at

Vx_final=Vx_initial+0(t)

Vx_final=Vx_initial= Vcos θ

Vertical component is Vy_initial= Vsin θ

Since gravity force is acting in vertical direction the acceleration(a) will be g

Using v²- u²=2as

s=h is the max height that the projectile will reach.

(i)for upward motion of projectile.

Final Velocity (i.e at the top point) will be zero.

0-(Vy_initial)²=2ah

a=-g

h= (Vy_initial)²/2g ……………….eqn(1)

(ii)for downward motion of projectile.

Initial velocity(i.e at the top point) will be zero

(Vy_final)²-0=2gh

Put value of h from eqn(1)

(Vy_final)²=2g((Vy_initial)²/2g)

Vy_final=Vy_initial= Vsin θ