Question #136111
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.
1
Expert's answer
2020-10-01T10:09:57-0400

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:

r1x=46  mr_{1x} = 46\;m

r2x=39  m×cos(47º)=39  m×0.68=26.52  mr_{2x} = 39\; m\times cos(47º) = 39\; m\times0.68 = 26.52\; m

rx=r1x+r2x=46  m+26.52  m=72.52  mr_x = r_{1x} + r_{2x} = 46 \;m + 26.52\;m = 72.52\; m

Displacement along the x-axis:

r1y=0  mr_{1y} = 0\; m

r2y=39  m×sin(47º)=39  m×0.73=28.47  mr_{2y} = 39\; m\times sin(47º) = 39\; m\times0.73 = 28.47 \;m

ry=r1y+r2y=0+28.47  m=28.47  mr_y = r_{1y} + r_{2y} = 0 + 28.47\;m = 28.47\; m

Pythagorean theorem:

r2=ry2+rx2r^2 = r^2_y + r^2_x

D=ry2+rx2=72.522+28.472=77.90  mD = \sqrt{r^2_y + r^2_x} = \sqrt{72.52^2 + 28.47^2} = 77.90 \;m

Answer: 77.90 m

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