Math CentralQuandaries & Queries


Question from Claire, a student:

An airplane flying at an altitude of 3500 feet is dropping supplies to researchers on an island. The path of the plane is parallel to the ground at the time the supplies are released and the plane is traveling at a speed of 300 mph.
a) write the parametric equations that represent the path of the supplies
c)How long will it take for the supplies to reach the ground?
d) how far will the supplies travel horizontally before they land?

Hi Claire,

Put a coordinate system on the plane with the origin on the ground, directly below the airplane at the instant the supplies are released. Suppose the position of the package $t$ seconds after it is released is $(x(t), y(t))$ where the distances are measured in feet. Convert 300 miles per hour to feet per second.

Consider the $y$ coordinate first. Looking only at $y$ and ignoring air friction you have $y(0) = 3500$ feet and the force operating on the package is the force due to gravity. What is the $y$ coordinate, $t$ seconds after it is released? What is the time $t$ when $y(t) = 0?$

Now consider the $x$ coordinate. Again ignoring air friction the package moves in the $x$ direction at a constant rate of 300 mph (in feet per second). Write this as an expression $x(t) = ???.$ What is the value of $x(t)$ when the package hits the ground?

I hope this helps,

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