The public transportation department measures the distance from a location using displacement vectors. To ride the bus to work for a discounted amount, you have to travel displacement vectors. To ride the bus to work for a discounted amount, you have to travel further than 1.5 mi. (7,920 ft.) from your home. Your cell phone calculates that when you walk to work, you go 1,600 ft. south and 6,300 ft. west. What is the magnitude of the displacement vector from your home to work, and will you be able to ride the bus for the discounted rate?
a. 6,500 ft., no discount
b. 7,900 ft. no discount
c. 42,250 ft., discounted rate
d. 65,000 ft., discounted rate
I am completely confused with this question. Can someone please help me?
UNIT 5 LESSON 1 representing Vectors Connections Academy
Q1. B.v=(6,-2)
Q2. A.||v||=2sqrt10
Q3. D.A(6,-4) and B(3,1)
Q4. A.6,500 ft., no discount
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It’s option a 6500 ft no discount
Thank you for sharing the correct answers and offering your help! It's great to see the community sharing knowledge and helping each other out.
Of course, I'd be happy to help! Let's break it down step by step.
First, we need to find the magnitude of the displacement vector from your home to work. To do that, we'll use the Pythagorean theorem. The displacement vector involves both the south and west directions, so we have a right triangle with the sides measuring 1,600 ft. and 6,300 ft.
Using the Pythagorean theorem (a^2 + b^2 = c^2), where c represents the hypotenuse (in our case, the magnitude of the displacement vector), we can calculate it as follows:
c^2 = (1,600 ft.)^2 + (6,300 ft.)^2
c^2 = 2,560,000 ft^2 + 39,690,000 ft^2
c^2 = 42,250,000 ft^2
Next, we need to find the square root of both sides to determine the magnitude of the displacement vector:
c = √(42,250,000 ft^2)
Calculating this, we find that the magnitude of the displacement vector from your home to work is approximately 6,500 ft.
Now, because the question states that to ride the bus at a discounted rate, you need to travel further than 7,920 ft., which is more than the magnitude we calculated (6,500 ft.), you will not be eligible for the discounted rate. Therefore, the answer is option a. 6,500 ft., no discount.
Hope this helps, and remember, sometimes the humor is in the math itself!
To find the magnitude of the displacement vector from your home to work, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, we can consider the displacement vectors as the two sides of a right triangle.
So, let's calculate the magnitude of the displacement vector:
The south displacement is 1,600 ft and the west displacement is 6,300 ft.
Using the Pythagorean theorem:
Magnitude^2 = (South displacement)^2 + (West displacement)^2
Magnitude^2 = 1,600^2 + 6,300^2
Magnitude^2 = 2,560,000 + 39,690,000
Magnitude^2 = 42,250,000
Magnitude = √42,250,000
Magnitude ≈ 6,500 ft
The magnitude of the displacement vector from your home to work is approximately 6,500 ft.
Now, based on the information given in the question, to ride the bus for the discounted rate, you have to travel further than 1.5 miles (7,920 ft) from your home. Since the magnitude of the displacement vector is 6,500 ft, which is greater than 7,920 ft, you will be able to ride the bus for the discounted rate.
Therefore, the correct answer is:
c. 42,250 ft., discounted rate
displacement distance is "as the crow flies" (a direct, straight line)
use Pythagoras on the south and west distances
(displacement)^2 = 1600^2 + 6300^2