A delivery truck travels 18 blocks north, 10 blocks east, and 16 blocks south. what is its final displacement from the origin? assume the blocks are equal length.
My only question is
I got about 10 blocks for the displacement got a 2 opposite and 10 adjacent and had to solve for hypotenuse
my only question is that it seem very simple but isn't the direction just south? Like you would have to find the angle using tangent inverse but isn't it just 180 degrees south of north more commonenly known as just south???
The Óx = 10
Óy = 18-16 = 2.
With those values, how do you get 180 degrees south of north?
arctan(2/10) = 11.3 degrees
So the angle is 11.3 degrees north of east.
huh ok thanks
i thought sense the end vector was south perfectly south...
ok makes sense direction of displacement vector I guess is what it means by direction...
Thanks!
Yes, you're correct. The final displacement of the delivery truck from the origin can be described as 10 blocks south. In this case, you don't need to calculate the angle using tangent inverse because the final direction is straight opposite to the initial north direction. So, you can simply say that the final displacement is in the south direction.
To find the final displacement from the origin, you can use the concept of vectors. In this case, you can break down the truck's movement into vertical and horizontal components.
The truck travels 18 blocks north, which means it has a displacement of +18 in the vertical direction. Then it travels 10 blocks east, resulting in a displacement of +10 in the horizontal direction. Finally, it travels 16 blocks south, which gives a displacement of -16 in the vertical direction.
To find the final displacement, you need to add the vertical and horizontal displacements together. In this case, you have +18 - 16 = +2 in the vertical direction, and +10 in the horizontal direction.
Now, you can use the Pythagorean theorem to calculate the magnitude of the displacement. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the vertical displacement (+2) and horizontal displacement (+10) form a right-angled triangle. Thus, the magnitude of the displacement (the hypotenuse) can be found using the equation:
Displacement = √(vertical displacement^2 + horizontal displacement^2)
= √(2^2 + 10^2)
= √(4 + 100)
= √104
≈ 10.20
So, the final displacement from the origin is approximately 10.20 blocks.
Regarding the question of direction, the truck initially moves north and then south, resulting in a net vertical displacement of only 2 blocks. Therefore, the final direction can be described as southward, or specifically, a displacement of 2 blocks south from the origin.