Question

A taxicab moves five blocks due north, five blocks due east, and another two blocks due north. Assume all blocks are of equal size. What is the magnitude of the taxi’s displacement, start to finish?

Answer 1

Answer: The magnitude is 8.66 blocks

Step-by-step explanation:

First, the cab moves 5 blocks to the north, after that, the cab moves 5 blocks to the east, and after that, the cab moves another 2 blocks to the north.

So the total displacement is 7 blocks to the north and 5 blocks to the east,

But the total displacement will be the hypotenuse of a triangle where the cathetus is those two values:

As you know, for the Pythagorean's theorem we have that:

H^2 = 7^2 + 5^2 = 49 + 25 = 74

H = (75)^(1/2) = 8.66 blocks

Then the magnitude of the taxi's displacement (the difference between the final position and the initial position) is 8.66 blocks

Answer 2

The total displacement north is 7 blocks. The total east is five blocks. What you're looking for is the hypotenuse length for a right triangle with sides of 5 and 7 blocks. Square 5, square 7, add the two results, then take the square root to get the length of the hypotenuse (the displacement) in "blocks". 25+49=74. Square root is between 8 & 9 blocks and that (you can make it exact) is the magnitude of the displacement of the taxi.