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# Equations of motion and their solutions

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An airplane is flying at 160km/hr 80 m above a level field. A rancher wants to drop a bale of hay such that it lands 30 m in back of the cattle (the cattle are facing away from the line of flight). The air resistance of the bale is .107*v^2(meters per seconds squared). Including the air resistance where should the rancher drop the bale so it lands 30m in back of the cattle?

Solve using manual integration and show all steps in detail and clearly.

##### Solution Summary

The solution shows how to solve thedifferential equations of motion when air resistance in two dimensions is considered.

##### Solution Preview

In the vertical direction, the equation of motion is:

Where g is the gravitational acceleration (we set "down" as a positive direction).

While in the horizontal direction the equation of motion is:

Where V is the plane's speed.

The horizontal equation is separable:

Using the initial ...

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