Question

I need the formula for calculating speed in a parabolic trajcetory with no air resistance. I need to reach a range of 20meters from a 45 degree angle. what speed do I need to be travelling at? I need the formula for future reference. Thank you.

Answer 1

Denote the angular of the speed vector to the horizontas α, the horizontal and vertical projections of theinitial speed as Vox and V_oy respectively. V_ox = V_o cos(α)
V_oy = V_o sin (α)
The equations of the motion:
V_y = V_oy - gt
H =H_o + V_oyt - gt²/2
S = V_ox t
For the case of α = 45, S = 20:
As sin(45) = cos(45) = √2/2 , Vox= √2/2 Vo = Voy
S = √2/2 Vo t = 20
t = 20√2 /Vo
As moving upward lasts only a half of motion time and at the highest point Vy =0,
V_oy = gt/2
√2/2 Vo =10* 20√2 /2Vo
Thus,
Vo² = 10* 20 = 200
Vo = 10√2