Question

6. An aircraft carrier travels north at 15 km/h. On its radar, the carrier spots an airplane flying 450 kmh to the northeast, relative to the ship. What are the magnitude of the plane's velocity relative to earth? What is the direction of the velocity?(Give an angle) CHECK: VA 460.73 kmh N0

Answer 1

Velocity of carrier v_B vector = 15 km/h North Velocity of airplane w.r.t carrier V_AB vector = 450 km/h North-East V_AB vector = V_A vector - V_B vector V_A vector = V_AB vector + V_AB vector angle b/w V_AB vector and V_B vector theta = 45 degree Vertical-bar v_A vector Vertical-bar = squareroot Vertical-bar v_AB vector Vertical-bar ^2 + Vertical-bar V_B vector Vertical-bar ^2 + 2 Vertical-bar V_AB vector Vertical-bar Vertical-bar V_B vector Vertical-bar cos theta = squareroot 450^2 + 15^2 + 2 times 450 times 15 times cos (45) = 460.73 km/h Vertical-bar v_A vector Vertical-bar = 460.73 km/h psi = tan^-1 [ Vertical-bar v_B vector Vertical-bar sin 45 degree/ Vertical-bar v_AB vector Vertical-bar + Vertical-bar v_B vector Vertical-bar cos 45] = tan^-1 [15 times sin (45)/450 + 15 times cos (45)] = 1.32 degree Angle of v_A vector from East r = 45 + phi = 45 + 1.32 = 46.32 degree Direction of V_A vector = 46.32 degree North of East