Starting at home a salesman drove 20km east, then 9km north, then 4km east. finally, he drove x km south and at that point he was exactly 25 km away from his home. find x.
d = 24km@0o+9km@90o+4km@0o+Nkm@270o.
Find N.
X = 20+4 = 24 km.
Y = (8-N)km
d^2 = X^2 + Y^2 = 35^2.
d^2 = (130^2+(8-N)^2 = 35^2
576+(N^2-16N+64) = 1225
N^2-16N+640-1225 = 0
N^2-16N-585 = 0
N = 33.475(Use Quad. Formula)
Oops! Name is Henry. Not anonymous.
To find the value of x, we can use the concept of vectors. We'll consider the east direction as positive x-axis and the north direction as positive y-axis. Let's break down the salesman's journey into vector components.
1. First, he drives 20 km east. This is equivalent to moving 20 units in the positive x-axis direction.
2. Then, he drives 9 km north. This is equivalent to moving 9 units in the positive y-axis direction.
3. Next, he drives 4 km east. This is equivalent to moving 4 units in the positive x-axis direction.
Now, let's calculate the vector components:
- The x-component: 20km + 4km = 24km (since 20km east + 4km east = 24km east)
- The y-component: 9km (since there is no change in the y-axis)
The total displacement vector (d) can be calculated using the Pythagorean theorem:
|d| = √(x^2 + y^2)
In this case, we have |d| = 25 km. So, we can substitute the values to find x:
25^2 = 24^2 + 9^2
Simplifying the equation:
625 = 576 + 81
625 = 657
This equation is false, which means our initial assumption about x must be incorrect. Therefore, there's no value of x that can satisfy the condition of being exactly 25 km away from home after the final displacement.