Question

Your school is 4 miles east and 1 mine south of your apartment there is a park 3 miles east and 4 miles south of your apartment estimate the distance between the park and your school

Answer 1

Answer:

The distance between of the park to the school is approximately 8.6 miles

Step-by-step explanation:

The given information are;

The location of the school from the house = 4 miles East and 1 mile South

The location of the park from the house = 3 miles East and 4 mile South

By representing the direction East (x-direction) as being in the direction of vector $\hat i$ and the direction South (negative y-direction)  as being in the direction of vector $\hat j$, we have;

The location of the school from the house = 4·$\hat i$ + $\hat j$

The location of the park from the house = 3·$\hat i$ + 4·$\hat j$

The distance, l, between the park and the school is given by the resultant of the two vectors as follows

$l_x$ = 4·$\hat i$ + 3·

$l_y$ = $\hat j$ + 4·

Therefore,

$l = \sqrt{l_x^2 + l_y^2} = \sqrt{7^2 + 5^2} = \sqrt{74} \approx 8.6 \ miles$

The distance between of the park to the school ≈ 8.6 miles.