Chapter 5, Problem 21A

For Questions 20—21, recall that the resultant V of two vectors A and B at right angles to each other is found using the Pythagorean theorem: $V=\sqrt{A^2+B^2}$

Calculate the speed of raindrops hitting your face when they fall vertically at 3 m/s while you're running horizontally at 4 m/s.

To determine

Magnitude of resultant velocity.

Answer to Problem 21A

Resultant velocity is, $v=5\text{ m/s}$

Explanation of Solution

Given :

Velocity in raindrop in vertical direction is, $v_y=3\text{ m/s}$

Velocity in horizontal direction is, $v_x=4\text{ m/s}$

Formula used :

The resultant of two vectors is,

  $R=\sqrt{A^2+B^2}$

Where, R is resultant vector, A and B are two vectors which are perpendicular to each other.

Calculation :

Both velocities are represented in below figure.

  

Here, both velocity are perpendicular to each other.

Therefore, their resultant velocity will be,

  $v=\sqrt{v_x^2+v_y^2}$

Now, substituting the value of $v_x$ and $v_y$ and solve.

  $\begin{array}{l}v=\sqrt{4^2+3^2}\\ =\sqrt{25}\\ =5\text{ m/s}\end{array}$

Conclusion :

Therefore, resultant velocity will be equal to 5 m/s.