Question #e7d7a

1 Answer
Jarni Renz
Jan 26, 2018

#=500m# at an average velocity of #(250m)/(min)# towards the NW

Explanation:

To answer this, one should be guided by the following facts that a displacement;

  1. is a straight line drawn from its original position to the object's final position.
  2. is a vector quantity; thus give attention to the direction of motion, but if the direction is one-dimensional motion; direction can be represented as positive or negative. Take note of the following:
    #"upward (north)=positive; downward (south)=negative"#
    #"left (west)=negative; right (east)=positive"#
  3. is not always equal to the distance being traveled.

This case, the car has traveled #300m" North(N)"#, #400m" West(W);,# and that, when we connect the initial position to its final position, apparently is forming a right triangle; thus, the
he concept of the Pythagorean Theorem can be applied to find the resultant length of the travel or its displacement.

#"Pythagoream theorem"# states that the square of the hypotenuse of a right triangle is equal to the squares of its legs; that is,

#c^2=a^2+b^2#

The length of the line that connects the final and initial positions of the car can be computed as;

#c=sqrt(a^2+b^2)#
where:

#c="the hypotenuse=the resultant length"#
#a="other leg=300m North"#
#b="other leg=400m West"#

#c=sqrt(300^2+400^2)#
#c=sqrt(90,000+160,000)#
#c=sqrt(250,000)#
#c=500m#

Therefore the displacement is #500m# at an average velocity of #(250m)/(min)# towards the #"Northwest"(NW)".#

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