A large passenger aircraft accelerates down the runway for a distance of 3000 m before leaving the ground. It then climbs at a steady 3.0° angle. After the plane has traveled 3000 m along this new trajectory, (a) how high is it, and (b) how far horizontally is it, from its initial position?

ANSWER: STEP 1:- Before leaving the ground the aircraft ran 3000 m on the ground. Then it got lifted with the angle of 3.0° and continued for 3000 m along the inclined trajectory. So schematically the problem looks like the figure given below. In the above diagram, A is the starting point of the aircraft. AB is the distance travelled before leaving the ground = 3000 m, 3° is the angle the aircraft made with the horizontal after leaving the ground, CD is the height the aircraft reached. BC is the distance covered through the new path after take off. STEP 2:- a) how high is it In the diagram, triangle BCD looks like a right angled triangle, whose hypotenuse and the angle we know. So by applying the laws of trigonometry, Let’s use the relation of, sin = perpendicular / hypotenuse 0 sin 3 = CD / BC 0.052 =...