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.
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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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