A jet flying at an altitude of 30,000 ft passes over a small...

Name: Problem 103, Chapter 3: Beginning and Intermediate Algebra
Uploaded: 2021-03-23T18:43:43-08:00
Duration: 6 min 16 s
Channel: Ruby P
Description: A jet flying at an altitude of 30,000 ft passes over a small plane flying at 15,000 ft headed in the same direction. The jet is flying twice as fast as the small plane, and 45 minutes later they are 150 miles apart. Find the speed of each plane.

A jet flying at an altitude of 30,000 ft passes over a small plane flying at 15,000 ft headed in the same direction. The jet is flying twice as fast as the small plane, and 45 minutes later they are 150 miles apart. Find the speed of each plane.

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Key Concepts

Relative Motion

This concept involves analyzing the movement of two objects with different speeds and directions to determine how their positions change relative to each other over time. In problems where objects travel in the same or opposite directions, understanding relative speeds is crucial for determining the net separation between the objects.

Distance-Speed-Time Relationship

A fundamental concept in kinematics is the relationship d = vt, where distance equals speed multiplied by time. This relationship is used to compute how far an object has traveled over a specific period, and it forms the basis for establishing equations when comparing the movements of different objects.

Unit Conversion

To maintain consistency in calculations, it is essential to convert units where necessary. For instance, when distances are given in feet and miles, converting feet to miles (or vice versa) ensures that all quantities are in compatible units before applying formulas or equations.

Pythagorean Theorem

When dealing with movements in two dimensions, such as when objects have both horizontal and vertical components of displacement, the Pythagorean theorem is used to calculate the straight-line distance between them. This theorem helps combine independent perpendicular distances to form a resultant separation distance.

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