Question

A jet airliner moving initially at 3.65 ✕ 10² mi/h due east enters a region where the wind is blowing at 1.00 ✕ 10² mi/h in a direction 26.0° north of east. (Let the x-direction be eastward and the y-direction be northward.)

3. -17 points | SERCP11 3.3.P.023. My Notes Ask Your Teacher v A jet airliner moving initially at 3.65 x 102 mi/h due east enters a region where the wind is blowing at 1.00 x 102 mi/h in a direction 26.0° north of east. (Let the x-direction be eastward and the y-direction be northward.) (a) Find the components of the velocity of the jet airliner relative to the air, VA VJA,x = mi/h VJA,Y = mi/h (b) Find the components of the velocity of the air relative to Earth, VAE VAE,x = mi/h VAE,y = mi/h (C) Write an equation analogous to VAB = VAE - Vse for the velocities VJA, VAE, and VJE: (In the given equation, Vee is the velocity of observer B relative to observer E. Object A travels with velocity Vag relative to observer B, and velocity VAE relative to observer E.) OVA = VAE + 2VJE OVA = VE + VAE OVA = VJE - VAE OVA = VAE - VE (d) What are the speed and direction of the aircraft relative to the ground? magnitude mi/h direction • north of east

Answer 1

Odlution - Solution:- U je - 3:65x10 milh UAE = 100 Xbo milh = 1.00 xlo mili Sinar A 1260 VE = 3.65 Xlo miste n Acos 26

@) velocity of our relative to Earth is UAE v Cos 26 i + VA Sin 26 ] = (100x12) (0.899) i +(1.00 x 15 ) (0.438) } VAL = ( 0. 899 x103 2 1 + 0.438 10 7 mil velocity of Jest relative to Earth in UJE = Use i to Je = 3.65x10 3 a mile -

Relative velocity of Jet auline with respect to an :- USA = UJE - BAE -3.65x1.32 - {0.899x180 + 0.438x10 f ] Ta = 2.751x1° 9 – 0:438x3°5 | mi/h So 0,= 2.751x1°mi/h Vony = -0-488xx" mily! (6) Tre - 60.89985° 9° 40-438 xbg) silne We x = 0.899x10 milh [UAE, y = 0.438x10 mi/h)

EA (c) DPB = PAC OBE So, A = UJE DAE (d) speed of aircraft relative to ground / Earth is DE = JA -JA = BA + VAE TE = (2.751x1829-0438x2°1)+ (639x12? +0 438x1°3) Tore = (2-75180° 40.931°) 2 + (-0438*18*40:438x18) } De = (3.65 x10 " to? I milh o je l = √ (365X23) ? to = 3.65 x1 mile direction : tamo = o. 3.65x16? O = tant (o) = 0 10=07 North of east.