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 290mph at an altitude of 900m . 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 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 = 9.80m/s^2 What is the speed of the package when it hits the ground?

Explanation / Answer

H=0.5gt^2 The time it takes for the package to fall is t=sqrt(2H/g) t=sqrt(2 x 900/9.81)=13.54s its horizontal speed will be same as before 290mph and verticle speed will be v = sqrt ( 2*g*H) = sqrt( 2*9.8 * 900) = 132.81 m/s

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