The Power of Displacement in Solving Distance Problems

Hello! Your Question:

A plane flies along a straight line path after taking off, and it ends up 210 km farther east and 90.0 km farther north, relative to where it started. What is the plane's displacement?

A. 300 km

B. 141 km

C. 230 km

D. 120 km

Answer:

210 + 90 = 300

Answer = A. 300 km

Final answer: The plane's displacement can be calculated using the Pythagorean theorem. Given that the plane has moved 210 km east and 90 km north, the displacement is approximately 225 km.

Explanation:

The displacement of the plane can be determined using the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a^2 + b^2 = c^2). We consider the plane's movement east and north as two sides of a right triangle, and the displacement as the hypotenuse. Therefore, in the given problem, a = 210 km (east) and b = 90 km (north). Substituting these values into the theorem formula, we get c^2 = (210 km)^2 + (90 km)^2. Solving this, we find c (displacement) to be approximately 225 km. Therefore, none of the multiple-choice options (A, B, C, or D) given in the problem are correct. The plane's displacement is 225 km.