Math Problem Statement

What is the total displacement, to the nearest tenth, of a car that travels 35 km north, then 20 km east?

Solution

The total displacement of the car can be found using the Pythagorean theorem. Since the car travels 35 km north and 20 km east, these two distances form the legs of a right triangle. The displacement is the hypotenuse of this triangle.

We can calculate the displacement dd using the formula:

d=(352+202)d = \sqrt{{(35^2 + 20^2)}}

Let's calculate that:

d=352+202=1225+400=162540.3 kmd = \sqrt{{35^2 + 20^2}} = \sqrt{{1225 + 400}} = \sqrt{{1625}} \approx 40.3 \text{ km}

So, the total displacement is approximately 40.3 km.

Do you want more details or have any questions?

Here are some related questions:

  1. What is the angle of the car's displacement relative to north?
  2. How would the displacement change if the car had traveled south instead of north?
  3. What would the total distance traveled (not displacement) be in this scenario?
  4. How would the displacement change if the car first traveled west instead of east?
  5. Can the displacement ever be larger than the total distance traveled?

Tip: Displacement is the shortest distance from the starting point to the endpoint, while distance is the total length of the path traveled.

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangles
Displacement

Formulas

Pythagorean theorem: a^2 + b^2 = c^2

Theorems

Pythagorean theorem

Suitable Grade Level

Grades 7-9