Answer to Question #136111 in Mechanics | Relativity for Isaiah marez

Question

A person walks 46 m East and then walks 39 m at an angle of 47 degrees North of East. What is the magnitude of the total dis-placement ? Answer in units of m.

Answer 1

We have two displacements: r₁ (when a person walks 46 m East), r₂ (when a person walks 39 m at an angle 47 degrees) and total displacement r.

Displacement along the x-axis:

$r_{1x} = 46\;m$

$r_{2x} = 39\; m\times cos(47º) = 39\; m\times0.68 = 26.52\; m$

$r_x = r_{1x} + r_{2x} = 46 \;m + 26.52\;m = 72.52\; m$

Displacement along the x-axis:

$r_{1y} = 0\; m$

$r_{2y} = 39\; m\times sin(47º) = 39\; m\times0.73 = 28.47 \;m$

$r_y = r_{1y} + r_{2y} = 0 + 28.47\;m = 28.47\; m$

Pythagorean theorem:

$r^2 = r^2_y + r^2_x$

$D = \sqrt{r^2_y + r^2_x} = \sqrt{72.52^2 + 28.47^2} = 77.90 \;m$

Answer: 77.90 m