Answer to Question #1371 in Mechanics | Relativity for frank

Question #1371
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.
1
Expert's answer
2011-01-22T11:10:00-0500
Denote the angular of the speed vector to the horizontas α, the horizontal and vertical projections of theinitial speed as Vox and Voy respectively. Vox = Vo cos(α)
Voy = Vo sin (α)
The equations of the motion:
Vy = Voy - gt
H =Ho + Voyt - gt2/2
S = Vox 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,
Voy = gt/2
√2/2 Vo =10* 20√2 /2Vo
Thus,
Vo2 = 10* 20 = 200
Vo = 10√2

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