Why does velocity along x axis not change as a function of time during projectile motion? U_x will be equal to u cos theta and u=sin theta. But in case of final velocity, it is v cos theta where −gt=0 and v sin theta−gt. Why is that ?

Bayobusalue

Bayobusalue

Answered question

2022-11-13

U x will be equal to u cos θ and u = sin θ. But in case of final velocity, it is v cos θ where g t = 0 and v sin θ g t
Why is that ? I am not getting how to solve this.

Answer & Explanation

Haylie Park

Haylie Park

Beginner2022-11-14Added 14 answers

The generic equation that describes your problem is
{ x ( t ) = v 0 cos θ 0 t y ( t ) = v 0 sin θ 0 t 1 2 g t 2 { v x = v 0 cos θ 0 v y = v 0 sin θ 0 g t .
Let's take a look at the final situation. y ( t ) is clearly zero, so
tan θ 0 x g x 2 2 v 0 2 cos 2 θ 0 = 0 x final = 2 v 0 2 cos 2 θ 0 tan θ 0 g = v 0 2 sin ( 2 θ 0 ) g
x final,max = v 0 2 g , θ 0 = π / 4  and  t final = v 0 2 / g sin ( 2 θ 0 ) v 0 cos ( θ 0 )
v y ( t final ) = v 0 sin θ 0 , v x ( t final ) = v 0 cos θ 0

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