A boat sails 251 km to the East and then 534 km to the North. What is the distance of the boat from its starting point?

Draw the two displacement vectors end to end. That will be like drawing the path on a map. Then draw the hypotenuse that connects the starting point of one with the end point of the other (the destination)

The distance from the starting point is the hypotenuse of that right triangle.

Remember Pythagoras?

To find the distance of the boat from its starting point, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the 251 km to the East and 534 km to the North form the two sides of a right triangle, with the distance of the boat from its starting point as the hypotenuse.

Using the Pythagorean theorem, we can calculate the distance:

Distance^2 = (251 km)^2 + (534 km)^2

Distance^2 = 63001 km^2 + 284556 km^2

Distance^2 = 347557 km^2

Taking the square root of both sides to solve for the distance:

Distance = √(347557 km^2)

Distance ≈ 589.67 km

Therefore, the distance of the boat from its starting point is approximately 589.67 km.