Question

show, from the first principles, that the equation of motion of a mass(m) on a spring , subject to a linear resistance force R, a restoring force S and a driving force G(t) is given by

Question 5 An aircraft is to fly from point A to and airfield B600 km due north of A. If a steady wind of 90 km/h is blowing from the north-west, find the direction the plane should be pointing and the time taken to reach Bif the cruising speed of the aircraft in still air 200 km/h

Question 5 An aircraft is to fly from point A to and airfield B600 km due north of A. If a steady wind of 90 km/h is blowing from the north-west, find the direction the plane should be pointing and the time taken to reach Bif the cruising speed of the aircraft in still air 200 km/h

Answer 1

Speed of the wind from the north west, v_w = 90 km/h speed of the acr craft, v = 200 km/h since, aircraft has to travel from south to North, speed along west - east duration should be zero v times sin theta - v_w cos 45 = 0 v times sin theta = v_w times cos 45 v times sin theta = 63.63 sin theta = 63.63/200 = 0.318 theta = sin^-1(0.318) = 18.54 degrees Now, speed along south - north direction is V^' = v cos theta - V_w times sin 45 degrees = 200 times cos (18.54) - 90 times 0.707 2w times 0.95 - 63.63 = 190-63.63 = 126.37 km/h let time taken, t v^' = d/t implies t = d/w = 600/126.37 = 4.75 s