Question 3
1 pts
During a race, you run east 5 kilometers and then turn north and run another 8 kilometers. What distance did you travel? What is your displacement from your start point?

Step 1 ：The total distance travelled is the sum of the distances travelled in each leg of the race. In this case, it's 5 km east and 8 km north.

Step 2 ：So, the total distance is \(5 km + 8 km = 13 km\).

Step 3 ：Displacement is a vector quantity that refers to 'how far out of place an object is'; it is the object's overall change in position.

Step 4 ：We can use the Pythagorean theorem to calculate the displacement, as the movement forms a right triangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: \(a² + b² = c²\).

Step 5 ：In this case, \(a = 5 km\) (east), \(b = 8 km\) (north), and \(c\) is the displacement we're trying to find.

Step 6 ：By substituting the values into the Pythagorean theorem, we get \(c = \sqrt{5^2 + 8^2} = 9.43 km\).

Step 7 ：Final Answer: The total distance travelled is \(\boxed{13}\) kilometers and the displacement from the start point is approximately \(\boxed{9.43}\) kilometers.