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 290 mph at an altitude of 750m . For all parts, assume that the "island" refers to the point at a distance from the point at which the package is released, D. Ignore the height of this point above sea level. Assume that the acceleration due to gravity is = 9.80m/s^2. t=2.4sec D=1600m v_0=290mph What is the speed of the package when it hits the ground in mph?

Explanation / Answer

Given horizontal speed of the aeroplane: u = 260 kmph = 72.22 m/s (assuming kmph since no units given) Altitude of the aeroplane h = 1000 m (assuming height in meters as no units given) We know the acceleration due togravity g = 9.8 m/s^2 Hence the time it will take to reach sea level is t = sqrt(2h/g) = 14.29 s Horizontal distance at which the package is to be released (range) R = u * t = 72.22 * 14.29 = 1032.02 m x-component of final velocity Vx = Horizontal velocity of aeroplane = u = 72.22 m/s and the y-component of finalvelocity Vy = - gt = - 9.8 X 14.29 = -140.042 m/s (downward direction) Hence the final velocity V = sqrt(Vx^2 + Vy^2) (on substituting the above values and simplifying) = 157.57 m/s

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