Mathematics 10 — Exercise Review · Q9

Full question

Find the magnitude of velocity 6î+8ĵ.

Step-by-step solution

1. The first component multiplies î, the second multiplies ĵ.

   $$6\times î+8\times ĵ$$

2. Use the horizontal and vertical components as the two perpendicular sides.

   $$\left[\begin{array}{c}6\\ 8\end{array}\right]$$

3. Magnitude is the nonnegative square root of the sum of component squares.

   $$\sqrt{6^2+8^2}$$

4. Square the horizontal component, including its sign.

   $$6^2=36$$

5. Square the vertical component, including its sign.

   $$8^2=64$$

6. Add these two squares.

   $$36+64=100$$

7. Take and simplify the positive square root.

   $$\sqrt{100}=10$$

Answer

The final answer is shown below.