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 260 at an altitude of 600 . 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 = 9.80 . After a package is ejected from the plane, how long will it take for it to reach sea level from the time it is ejected? Assume that the package, like the plane, has an initial velocity of 260 in the horizontal direction

Explanation / Answer

Hi, 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 Note: Since units are not mentioned in the problem, I have taken some relavent units and done the prob. If you have a different units, convert them into the units shown in the prob and follow the same method to get the corresponding answers. Hope this helps you. Note: Since units are not mentioned in the problem, I have taken some relavent units and done the prob. If you have a different units, convert them into the units shown in the prob and follow the same method to get the corresponding answers. Hope this helps you.

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