Question #4cf43

We're asked to find the total distance an object travels given the time and the components of its (constant) velocity.

To do this, we can use the time and each velocity component to find the components of its position, using the simple velocity equation

`overbrace("velocity")^"(constant)" = "displacement"/"time"`

We can split this into `x`- and `y`-components, taking east to be the positive `x`-direction, and north to be the positive `y`-direction:

`v_x = (Deltax)/(Deltat)` Solving for position: `Deltax = v_x(Deltat)`

`v_y = (Deltay)/(Deltat)` Solving for position: `Deltay = v_y(Deltat)`

We know:

• `v_x = -40` `"m/s"` (west is negative direction)

• `v_y = -70` `"m/s"` (south is negative direction)

• `Deltat = 20` `"s"`

Plugging in known values:

`Deltax = (-40"m"/(cancel("s")))(20cancel("s")) = color(red)(-800` `color(red)("m"`

`Deltay = (-70"m"/(cancel("s")))(20cancel("s")) = color(green)(-1400` `color(green)("m"`

The total distance traveled can be found using the distance formula:

`r = sqrt((Deltax)^2 + (Deltay)^2) = sqrt((color(red)(-800)color(white)(l)color(red)("m"))^2 + (color(green)(-1400)color(white)(l)color(green)("m"))^2`

`= color(blue)(1612` `color(blue)("m"`

Which if you wish to round to only `2` significant figures, is

`color(blue)(1600` `color(blue)("m"`