Question

After taking off, a helicopter climbs in a straight line at a constant angle β. Its flight is tracked by radar from point A. Determine the speed and acceleration of the helicopter in terms of d, β, θ, and θ

B В A d -

Answer 1

solution From triangle ABC 0+ (180-3)+Q;&0" SA QY BV Y 140 a ß- 10 Apply sine tule Y sin (190. p) Sind Substitute B-O for a 1 sin (190-1) Sin (ß-0) d sinß sin (ß-0) Angular component of velocity vo dsing sin (ß-0) v Sirda dsin ß Sin (B-0) ro ó

:(de B-0) vsin(B-0) VE speed of helicoptea of velocity dooivative using gadial component r = dr dr do o do dt dr do substi dt Divide both numewator & denominatoa = do tarp tan oso - Sine) dsinß Sn (3-0) dsing sin? CB-0) e) a sink tituting Sin (B-o) Sin (ß-o) d sing d do by cosp" r = 2 d for r. dsinfo] 0 d do o 8 dsinf Scos e (singcos o - cospsinb)/COSB cose] do tang to [ tanplase - Sine *(tanp(-sine) coses smo acoso cose - Sing)? - do tanp [ tang (tanp

Jadial Vcos da -Stanß tanp3 sino + coso v (cosp caso + Sinp sino) - dó tarp Carpcoso -sino) sides. substitute v cosa for v by the Component of velocity in the diagram. do tan tanßsino + coso coso - sino)? : (Q= B-0) V cos (B-0) - do tompL (tanß coso-sino (tanpsi n87650 Divide with cosp on both do tanß Cose Cosp tanp sino + coso (tanp.coso - Sino)2 v (cose + tanp Sing) – do'tan Seeßx cose + tanpsino (tanpcoso - sino) tank x v cosp cose 4 simpsine Liela ) [ s do tanß seep VE (tarß cose- sino)?