A taxicab moves 5 blocks due north, 5 blocks due east, and another 2 blocks due north. Assume all blocks are of equal size. What is the magnitude of the taxi's displacement?
north 7 and east 5
hypotenuse
sqrt(49+25)
To find the magnitude of the taxi's displacement, we can use the Pythagorean theorem.
The taxi moved 5 blocks due north and then 2 blocks more due north, so the total displacement in the north direction is 5 + 2 = 7 blocks.
The taxi also moved 5 blocks due east, so the displacement in the east direction is 5 blocks.
Now, we can use the Pythagorean theorem to find the magnitude of the displacement. The magnitude is equal to the square root of the sum of the squares of the displacements in each direction.
Magnitude of displacement = √( north displacement^2 + east displacement^2 )
Plugging in the values, we have:
Magnitude of displacement = √( 7^2 + 5^2 )
= √( 49 + 25 )
= √74
≈ 8.60 blocks
Therefore, the magnitude of the taxi's displacement is approximately 8.60 blocks.
To find the magnitude of the taxi's displacement, we need to calculate the straight-line distance between the starting point and the ending point.
Let's break down the taxi's movements into components. Moving 5 blocks due north followed by 5 blocks due east can be represented by a displacement vector of (+5, +5) since the blocks to the north are represented by positive values and blocks to the east also have positive values.
Next, the taxi moves another 2 blocks due north, which can be represented by a vector of (+2, 0) since there is no movement in the east direction.
To find the overall displacement vector, we can sum the individual vectors. Adding (+5, +5) and (+2, 0) gives us (+7, +5).
Now, we can find the magnitude of the displacement vector. The magnitude of a vector is given by the square root of the sum of the squares of its components.
In this case, the magnitude of the displacement vector is:
sqrt((7^2) + (5^2))
= sqrt(49 + 25)
= sqrt(74)
Therefore, the magnitude of the taxi's displacement is sqrt(74) blocks.