Find the average velocity of a projetile between the instants it crosses half the maximum heght.It is projected with a speed u at an angle ø(thita) with horizontal.

Answer 1

I'm assumng you want the average velocity between hmax/2 and hmax.

Let theta = A.

Vo = u @ A deg. = Initial velocity.
Yo = ver = u*sinA = Vertical component.

Vf^2 = V0^2 + 2gh,
hmax = (Vf^2-V0^2) / 2g,
hmax=(0 - Yo^2) / -19.6 = Yo^2 / 19.6.

hmax/2 = 1/2(Yo^2/19.6) = Yo^2/39.2.

Vf^2 = Yo^2 + 2gh,
Vf^2 = Yo^2 + 2*(-9.8)(Yo^2/39.2),
Vf^2 = Yo^2 - 19.6(Yo^2/39.2),
Vf^2 = Yo^2 - Yo^2 / 2,
Vf^2 =0.5Yo^2,
Vf = 0.354Yo = velocity @ 0.5hmax.

Vf = 0 @ hmax.

Vavg = (0.354Yo + 0) / 2 = 0.177Yo.