100&101 - Required If a = 0 what must = q...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
TAM 212 Spring, 2004 1.100 Given: For the airplane shown, we know ( 29 D r r = , , q q ; the speed and the altitude are constant Required: What is the speed in terms of what we know? Solution: We can use k e e v z r r r + + = q q . We know r = D, and theta and its derivatives, and we know z and its derivatives are = 0, but we don’t know dr/dt. However, we can use the constraint the height of the airplane, H is constant, and ( 29 q q q q q q q cos sin 0 sin sin 0 sin sin r r dt d r dt dr r dt d H dt d r H + = + = = = q q cot r r - = , so ( 29 q q q q e e v r r r + = cot , and the speed ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 q q q q q q q q q q sin 1 sin / cos 1 cot cot 2 2 2 2 r r r r r = + = + = + = v ( 29 q q sin r = v 1.101 Given: At the instant shown, r = 3 in; s in r / . 4 = , and 2 / 5 s in r = . (z and its derivatives are zero.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Required: If a = 0, what must ? , = q q & & & Solution: We can use k e e a z r r r r r & & & & & & & & & + θ + θ + θ-= θ ) 2 ( ) ( 2 . For a = 0, both 2 =-q & & & r r and 2 = + q q & & & & r r For 2 =-q & & & r r , ( 29 s rad in s in / 3 / 5 3 / 5 2 2 ± = ⇒ =-q q & & For 2 = + q q & & & & r r , ( 29 ( 29 ( 29 ( 29 2 / 3 / 5 3 / 8 / 3 / 5 / 4 2 3 s rad s rad s in in ±-= ⇒ = ± + q q & & & & i.e., ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 / 3 / 5 3 / 8 , / 3 / 5 , , / 3 / 5 3 / 8 , / 3 / 5 , s rad s rad s rad s rad-=-= q q q q & & & & & & or...
View Full Document

Ask a homework question - tutors are online