Vectors and Projectiles - Mission VP4 Detailed Help

An ant walks 3.3 meters due west and then 1.7 meters due north. The magnitude of the ant's displacement is ___ meters. Enter a numerical answer accurate to the second decimal place. 
 
(Note: Numbers are randomized numbers and likely different from the numbers listed here.)


 
The head-to-tail method of vector addition can be used to create a rough sketch of this physical situation. The first vector (3.3 meters, west) is sketched (not to scale) in its indicated direction. The second vector (1.7 meters, north) is then sketched (not to scale) starting at the head (arrowhead) of the first vector. The resultant vector is then drawn from the tail of the first vector to the head of the last vector. The Pythagorean Theorem can then be used to calculate the magnitude of the resultant (see Math Magic section).


 
Pythagorean Theorem
When two vectors that make a right angle to each other are added together, the resultant vector is the hypotenuse of a right triangle. The Pythagorean theorem can be used to calculate the magnitude of the resultant. If the right triangle has sides with lengths of x and y, then the length of the hypotenuse is the square root of the sum of the squares of the sides. That is,
 
hypotenuse = SQRT (x2+ y2)


 
An effective strategy for all questions in this mission will center around a rough sketch of the addition of two vectors (See Think About It section). Consider the following steps:
 
  • Sketch the first vector in the appropriate direction. Place an arrowhead at the end of the vector.
  • Starting at the arrowhead of the first vector, draw the second vector in the appropriate direction and to the approximate length. Put an arrowhead at the end of the vector.
  • Draw the resultant vector from the tail of the first to the arrowhead of the second vector. Label the vector as R (for resultant) and put an arrowhead at the end of the resultant vector.
  • Since the resultant is a hypotenuse of a right triangle, the Pythagorean theorem can be used to calculate its magnitude (see Math Magic section).


 

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