A relief airplane is delivering a food package to a group of people stranded on

Question

A relief airplane is delivering a food package to a group of people stranded on a very small island. The island is too small for the plane to land on, and the only way to deliver the package is by dropping it. The airplane flies horizontally with constant speed of 270mph at an altitude of 600m . The positive x and y directions are defined in the figure. For all parts, assume that the "island" refers to the point at a distance D from the point at which the package is released, as shown in the figure. Ignore the height of this point above sea level. Assume that the acceleration due to gravity is g = 9.80m/s^2. What is the speed v_f of the package when it hits the ground?

Explanation / Answer

given the velocity of the plane = 270mph = 120.70 m/s 1) Let the packet take t sec to fall the vertical height of 550 m =>By s = ut + 1/2gt^2 => 600 = 0 + 1/2 x 9.8 x t^2 =>t = v112.24 =>t = 10.59 sec 2) By D = [Ux] x t =>D = 120.70 x 10.59 = 1278.76 m 3) By v = u + gt =>Vy = 0 + 9.8 x 10.59 = 103.78 m/s & Vx = Ux = 120.70 (horizontal component of velocity will remain constant during the flight of packet) =>v = v[(Vx)^2 + (Vy)^2] =>v = v[(120.70)^2 + (103.78)^2] =>v = 159.18 m/s =>v = 356.08 mph

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