# Raindrops are falling vertically at a speed of 120 km/h through air that is moving horizontally at a speed of 40 km/h(i.e. the wind is 40 km/h). How fast are the drops actually going?

Aug 8, 2017

$\text{speed} = 126.491$ $\text{km/h}$

#### Explanation:

We're asked to find the speed of the raindrops relative to a still observer (called an inertial frame of reference in physics).

We're given that the raindrops have a vertical speed of $120$ $\text{km/h}$ (downward, although direction doesn't matter) and a horizontal speed of $40$ $\text{km/h}$.

The magnitude of the speed is found by the distance formula:

$v = \sqrt{{\left({v}_{x}\right)}^{2} + {\left({v}_{y}\right)}^{2}}$

We have:

• ${v}_{x} = 40$ $\text{km/h}$

• ${v}_{y} = 120$ $\text{km/h}$

The speed of the raindrops is thus

$v = \sqrt{\left(40 \textcolor{w h i t e}{l} \text{km/h")^2 + (120color(white)(l)"km/h")^2) = color(blue)(ulbar(|stackrel(" ")(" "126.491color(white)(l)"km/h"" }\right) |}$