While picking up passengers in a big city, a taxi driver drives 20.0 blocks south, then 15.0 blocks east, and then 6.0 more blocks south. What is the magnitude of the taxi’s resultant displacement?
Iv'e been using the equation sqrt(x^2+y^2+z^2)
THe answer I get is 25.7, however, this is wrong. Please help!
why do you include a third dimension? The taxi cannot travel vertically.
The total displacements are
20+6=26 blocks south
15 blocks east.
So, √(15^2+26^2) = √901 = 30.0
To solve this problem, we need to find the resultant displacement of the taxi. The magnitude of the resultant displacement can be calculated using the Pythagorean theorem, but in this case, we are dealing with a two-dimensional problem (north-south and east-west directions) so the equation you mentioned is not applicable.
Instead, we can break down the problem into its vertical (north-south) and horizontal (east-west) components, and then calculate the magnitude of the resultant displacement using vector addition.
Let's break down the problem step by step:
1. The taxi drives 20.0 blocks south. This means the vertical component of the displacement is -20.0 blocks (negative because it's south).
2. The taxi then drives 15.0 blocks east. This means the horizontal component of the displacement is +15.0 blocks.
3. Lastly, the taxi drives an additional 6.0 blocks south, adding to the vertical component of the displacement. So the vertical component becomes -20.0 + (-6.0) = -26.0 blocks.
Now, we have the vertical and horizontal components of the displacement:
Vertical component: -26.0 blocks
Horizontal component: +15.0 blocks
To find the resultant displacement, we need to find the magnitude of the resultant vector by using the Pythagorean theorem:
Magnitude of the resultant displacement = sqrt((vertical component)^2 + (horizontal component)^2)
Magnitude = sqrt((-26.0)^2 + (15.0)^2)
Magnitude = sqrt(676 + 225)
Magnitude = sqrt(901)
Magnitude ≈ 30.0 blocks
Therefore, the correct magnitude of the taxi's resultant displacement is approximately 30.0 blocks.