Projectile motion velocity question

[J-dizzal]

Is the x component of the initial velocity equal to the velocity of the projectile at max height?

v₀cosθ₀i = v_{max height}i

 

[PFuser1232]

Is the x component of the initial velocity equal to the velocity of the projectile at max height?

v₀cosθ₀i = v_{max height}i

Yes it is. The $x$-component never changes since there is no acceleration in the $x$-direction. At maximum height, $v_y = 0$, so $\vec{v} = v_0 \cos{\theta_0} \hat{\imath}$.

 

[gsal]

we are talking in vacuum, right?

 

[J-dizzal]

we are talking in vacuum, right?

yes that is the assumption

 

[AYPHY]

well if want to solve in real world then you have to consider drag force of air which will act on both x and y component and if wind is also blowing then it will effect the answer more but in ideal case as there is no acceleration along x direcion so dv/dt is 0 so velocity along x (v0 cos(angle of projection from horizontal) does not changes.