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 332 km/hour at an altitude of 975 m . 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 = 9.80 m/s2 .

After a package is dropped from the plane, how long will it take for it to reach sea level from the time it is dropped? Assume that the package, like the plane, has an initial velocity of 332 km/hour in the horizontal direction.Express your answer numerically in seconds. Neglect air resistance

If the package is to land right on the island, at what horizontal distance Dfrom the plane to the island should the package be released?Express the distance numerically in meters.

What is the speed vf of the package when it hits the ground?Express your answer numerically in meters per second.

Explanation / Answer

part a:

motion in vertical direction:

initial speed=0 m/s

acceleration=-9.8 m/s^2

distance travelled=-975 m

if time taken is t seconds

then using the formula:

distance covered=initial speed*time+0.5*acceleration*time^2

==>-975=0-0.5*9.8*t^2

==>t=14.106 seconds

part b:

horizontal speed=332 km/hr=92.222 m/s

horizontal distance travelled=horizontal speed*time

=92.222*14.106=1300.8867 m

so D should be 1300.8867 m

part c:

horizontal speed will remain constant at 92.222 m/s

vertical speed=initial vertical speed+acceleration*time

=0-9.8*14.106

=-138.2388 m/s

so total speed=sqrt(horizontal speed^2+vertical speed^2)

=166.1772 m/s

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