Question

An object moves from point D to point B and then to point F. What is its displacement? Round your answer to two significant figures. A) 0 m B) 6.4 m C) 9.2 m D) 15.6 m

Answer 1

An object moves from point D to point B and then to point F is 6.4 m.

Thus the correct option is (B).

Step-by-step explanation:

In order to determine the displacement from point D to point B and then to point F, we need to consider the vector sum of the individual displacements. Displacement is a vector quantity, meaning it has both magnitude and direction. Let's denote the displacement from D to B as Δ₁ and from B to F as Δ₂. Thus the correct option is (B).

The displacement is given by the vector sum:

`\[ \text{Displacement} = \Delta₁ + Δ₂ \]`

Now, to find Δ₁ and Δ₂, we can use the formula for displacement:

`\[ \text{Displacement} = √((\Delta)² + (\Delta)²) \]`

where Δ and Δ are the changes in position in the horizontal and vertical directions, respectively.

For the displacement from D to B:

`\[ Δ₁ = √((_B - _D)² + (_B - _D)²) \]`

And for the displacement from B to F:

`\[ Δ₁ = √((_B - _D)² + (_B - _D)²) \]`

By calculating these displacements and summing them up, we find the total displacement from D to B and then to F. After rounding the final answer to two significant figures, the correct option is B) 6.4 m.