Chapter 3, Problem 1OQ

What is the magnitude of the vector $(10\hat{\text{i}}\text{ - 10}\hat{\text{k}}\text{) m/s?}$(a) 0 (b) 10 m/s (c) −10 m/s (d) 10 (e) 14.1 m/s

To determine

The magnitude of the vector $\left(10\widehat{\text{i}}\text{-10}\widehat{\text{k}}\right)\text{m/s}$.

Answer to Problem 1OQ

The magnitude of the vector $\left(10\widehat{\text{i}}\text{-10}\widehat{\text{k}}\right)\text{m/s}$ is $14.1\text{m/s}$.

Explanation of Solution

Write the formula for the magnitude of a vector.

    $v=\sqrt{v_x^2+v_y^2}$

Here, $v$ is the velocity, $v_x$ is the x-component of the velocity, $v_y$ is the y-component of the velocity.

Conclusion:

Substitute $10\text{m/s}$ for $v_x$, $-10\text{m/s}$ for $v_y$ to determine the magnitude of the vector.

    $\begin{array}{c}v=\sqrt{{\left(10\text{m/s}\right)}^2+{\left(-10\text{m/s}\right)}^2}\\ =14.1\text{m/s}\end{array}$

The magnitude of the vector $\left(10\widehat{\text{i}}\text{-10}\widehat{\text{k}}\right)\text{m/s}$ is $14.1\text{m/s}$.