question about 3 particular motion Your roommate has convinced you to take up sk

Question

question about 3 particular motion

Your roommate has convinced you to take up skydiving. He says that the
Jim Wallace School in Lake Perris is the place to go because you don't
have to go tandem on your rst jump. So on the chosen day, you take
the drive north and take the course and so you're all ready to jump.

Your roommate is going for the AFF Level Two while you are going for the AFF
Level One. Since he'll be tracking during his jump, while you'll maintain
the arch position during yours, his terminal speed will be 1.5 times faster
than yours. Since the two of you are about the same size and are required
to wear similar freaky Evel-Knievel-looking jumpsuits, it's reasonable to
assume that you both have the same drag coecient, C. If your roommate
weighs 20% more than you do, show that the tracking-posture and arch-
position cross-sectional areas are related by

Explanation / Answer

let m1= you

let m2 = roomie = (12/10)m1 , because they weigh 20% more than you.

first set up eqtn for you [ m1 ]:

because a = 0 at term velocity

F= m1a =0

0 = D - m1g

D = m1g

set up eqtn for roomie [ (12/10)m1 ]:

because a = 0 at term velocity

F= m2a = (12/10)m1a =0

0 = D - (12/10)m1g

D = (12/10)m1g

let D = (1/2)CpAav^2 for you

let D = (1/2) CpAtv^2 for roomie

plug in for both eqtns and solve to terminal velocity

term vel. for you = vt1

term. vel. for roomie = vt2

vt1 = sqrt [ (2m1g) / (CpAa) ]

vt2 = sqrt [ 2(12m1g) / (10CpAa) ] => sqrt [ (12m1g) / (5CpAa) ]

because your roomie's vt2 is 1.5 times greater than your vt1.

let --> (3/2)vt1 = vt2

plug in vt1 and vt2, SOLVE FOR At, which is the cross-swctional area for roomie.

---->>>>>algebra

square both sides

cancel out m1g on tops

cancel out Cp on bottoms

should get to (18 / 4Aa) = (12 / 5At)

(18 /4)At = (12 /5)Aa

At = (12/5)(4/18) Aa = (2/5)(4/3) Aa = (8/15) Aa

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