Edmond H.
asked 11/03/21Solving Equations - Projectile Motion
Using these 2 equations:
1) x = (vox * t) + (½ ax * t^2) = (vo * t)
2) y = (voy * t) + (½ ay * t^2) = (-½ g * t^2)
Show that this equation is correct:
vo = D ( g / ( 2 H ) )^½
1 Expert Answer
Sidney P. answered 11/06/21
Minored in physics in college, 2 years of recent teaching experience
I have reverse-engineered the context of this problem in which the comment I wrote doesn't apply: The context is an object rolling off or being fired horizontally at speed vo from a table or cliff, where H is the height of the table or cliff and D the horizontal distance travelled before hitting the floor or ground.
D = vo t, t = D/vo. The vertical displacement is negative, y = -H. -y = 1/2 g t2 = H, t2 = 2H/g, t = √(2H/g).
Setting the two times equal, D/vo = √(2H/g), vo = D / (2H/g)1/2 = D • (g/2H)1/2.
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Sidney P.
For projectile motion, equation 2 does not reduce to (-1/2 g t^2), you need to include voy. Equation 1 has a typo in right-hand term, should be vox. Without these corrections, height H = 0 and the solution is infinite!11/06/21