Question

(12) Relative Motion with respect to Translating Axes Two planes A and B are flying side by side at a constant speed of 900 km/h. Maintaining this speed, plane A begins to travel along the spiral path r = (15008) km, where is in radians, whereas plane B continues to fly in a straight line. Determine the velocity of plane A with respect to plane B when r = 750 km. If it is known that i' and ö are equal to zero for this instant, also determine the acceleration of A with respect to B. r= 15000 A/B = 18080.6ē, +9030.14@g, A/B = -111.63ē, + 446.52eo

Answer 1

Solution & Given that Consider the expression Y215000 for the path of plane A Substitute 750km for o. 750 =15000 O=0.5 rad x 180° ir A with respect to radial = 28.640 The direction of relocity of plane axis using the relation, w 8 1 doldo tan = = 15000 1500 Substitute 0-5 dati foro.. tan u 20.5 p=tan (0.5) =26.570 The direction of relocity A with respect to radial the path of B using the relation O + 8 = 88.64 +26-570 :56.21°

calculative the relative velocity of a with respect B using the relation VA EVB AVALB Substitute 900 (Cos 55.21% +51955-21°j) kmin foora and quiker for ve 900 cos 55.210; +900 sin 55.21 j = 900it VAIR VAIB = 6386-52; ++39.(53) Koln Calculate the magnitude of the velocity. VAIB = J 6-386.59) ² + 739.8 = 834 kmly the magnitude of the Velocity of a with respect to B is lo34 km/h) of the Calculate the direction the relation, o-tant relative velocity using 34 A - 386-52 .. 62.40 the direction of the relative with orespect to Bis 162.40 velocity of a