Question

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?

Answer 1

`"speed" = 126.491` `"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` `"km/h"` (downward, although direction doesn't matter) and a horizontal speed of `40` `"km/h"`.

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

`v = sqrt((v_x)^2 + (v_y)^2)`

We have:

• `v_x = 40` `"km/h"`

• `v_y = 120` `"km/h"`

The speed of the raindrops is thus

`v = sqrt((40color(white)(l)"km/h")^2 + (120color(white)(l)"km/h")^2) = color(blue)(ulbar(|stackrel(" ")(" "126.491color(white)(l)"km/h"" ")|)`