Answer :
Final answer:
Jessica's displacement after running 4000 m south and then 3 km east, following two legs that form a right triangle, can be calculated using the Pythagorean theorem to be around 5 km towards southeast.
Explanation:
Jessica's displacement can be determined using the Pythagorean theorem which states: the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b) - c^2 = a^2 + b^2.
Jessica first runs 4000 meters directly south and then 3 kilometers (or 3000 meters) directly east, each making a right angle with the other.
The displacement (d), which is the shortest distance between her starting and ending points, is the hypotenuse of the right triangle formed by these two legs.
By substituting a=4000 and b=3000 into the above formula, we get: d^2 = 4000^2 + 3000^2, and thus d = sqrt(4000^2 + 3000^2) = approx. 5000 meters or 5 kilometers.
Therefore, Jessica's displacement from her original position would be about 5 kilometers southeast.
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