# A vector drawn 50 mm long represents a velocity of 35 m/s. How long should you draw a vector to represent a velocity of 5 m/s?

mwmovr40 | Certified Educator

The essence of representing vectors by graphing is to make sure you have a clear idea of what the scale of the drawing is to be.  The scale is is the factor you use to transfer the vector to the graph in such a way that the drawing is proportional to the original vector.  The scale makes it practical to draw the vector (without a scale, to draw a 35 m vector would require a piece of paper 35 meters long!).

In this problem a 35 m/s velocity vector is being represented by a 50 mm arrow on a graph.  To get the scale, divide the length of the original vector by the length of the drawn arrow:

(35m/s)/(50mm) = 0.70m/s per mm.  This means that when you draw 1 mm long line on the paper it represents a vector of 0.70 m/s

The same scale must be used for every vector drawn on that graph.  To get the length of the line to represent any other vector we simply divide the size of the vector by the scale:

(5m/s)/(0.70m/s /mm)

Remember that dividing by a fraction is the same as multiplying by the reciprocal of the denominator:

(5m/s)X(1mm/0.7m/s) = 7.1 mm.

mwmovr40 | Certified Educator

An alternate way determine the length of the second vector to draw would be using the rules of proportions:

50 mm to 35 m/s has to be the same as Xmm to 5 m/s

We can rewrite these as ratios (dropping the units temporarily to make the math clearer.)

50/35 = X/5

We can solve for the length X by either doing cross multiplication-division:

50x5/35 = x

or notice that the 35 is reduced by a factor of 7 to get down to 5 therefore the 50 must be reduced by the same factor so

X = 50/7

In any case you get X = 7.1 mm.