Math CentralQuandaries & Queries


Question from beth, a student:

An airplane flies west at a speed of 200m/s. A package of supplies is dropped from the plane to some campers. if the plane is at an altitude of 1000meters, how far from the campers should the package be dropped to land near them? ignore wind resistance.

Hi Beth. Once the package leaves the airplane, the only force acting on it is gravity (since we are ignoring wind). Thus there is no change in the horizontal velocity of the package: it is the same as the airplane's speed and direction. To find the horizontal distance when you know the speed, you need to know the time it spends in the air.

To find the time it spends in the air, you can use your knowledge of the initial vertical speed (0 m/s), the vertical acceleration (g) and the vertical distance from the altitude the package left to the plane to the ground where it lands (1000 m). The formula for this is d = v0t + gt2, but since v0 is zero, that's just d = gt2. Solve for t and substitute the values in for g and d.

Hope this helps,
Stephen La Rocque.

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