Question

1. what is the magnitude of the resultant of a 3.0 - meter displacement and a 4.0 - meter displacement as shown in the diagram?

Explanation:

Step1: Identify the formula

We use the Pythagorean theorem for two - perpendicular displacements. If two displacements $a$ and $b$ are perpendicular, the magnitude of the resultant displacement $R$ is given by $R=\sqrt{a^{2}+b^{2}}$.

Step2: Substitute the values

Here, $a = 3.0$ meters and $b=4.0$ meters. So, $R=\sqrt{(3.0)^{2}+(4.0)^{2}}$.

Step3: Calculate the squares

$(3.0)^{2}=9$ and $(4.0)^{2}=16$. Then $R=\sqrt{9 + 16}$.

Step4: Calculate the sum inside the square - root

$9+16 = 25$. So, $R=\sqrt{25}$.

Step5: Calculate the square - root

$\sqrt{25}=5.0$ meters.

Answer:

5.0 meters