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Home Minds On Vectors and Projectiles Mission VP3 Vector Addition Applications Help Help 4

Mission VP3 Vector Addition Applications

The Question

A 5-ton airplane normally flies at 200 km/hr. If it experiences a 50 km/hr headwind (i.e., a wind coming 'head-on'), then its resultant velocity will be ...
 
(Note: the numbers in this question are random and will vary.)

Think About It

Think about this: you have likely run into the wind (headwind) and with the wind (tailwind) at some time in your life. A headwind makes your resulting speed less and a tailwind makes your resulting speed more. The same is true of a plane that is experiencing a headwind or a tailwind.
 
In this question, the tailwind must give the plane a greater resultant velocity. This rules out several options. To determine the correct option from among the remaining choices, simply add the two vectors, with one vector being in the opposite direction as the other (see Know the Law section below).

Physics Rules

Vector Addition - Head to Tail Method
The head-to-tail method of vector addition is one of several methods used to determine the resulting sum of two vectors. In this method, the first vector (the plane velocity) is drawn. The second vector (the wind velocity) is then drawn starting at the head of the first vector. For a head wind, the wind velocity vector would be drawn in the opposite direction as the plane velocity. The resultant vector stretches from the tail of the first vector (plane velocity) to the head of the last vector (wind velocity). Since the two vectors lie along the same line and in opposite directions, the vector addition can be done usingstraightforward addition of a negative vector to a positive vector.

Don't be Fooled

Many students of Physics form the impression that every given numerical value must be used in a calculation. But don't be fooled! The fact that the airplane is a 5-ton airplane is of no importance in this question. Always use your understanding of physics principles and relationships to develop the skill of discerning the importance and unimportance of given information.

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