Answer :
Answer:
(a) 1294.66 m
(b) 88.44°
Explanation:
d1 = 580 m North
d2 = 530 m North east
d3 = 480 m North west
(a) Write the displacements in vector forms
[tex]\overrightarrow{d_{1}}=580\widehat{j}[/tex]
[tex]\overrightarrow{d_{2}}=530\left ( Cos45\widehat{i}+Sin45\widehat{j} \right )[/tex]
[tex]\overrightarrow{d_{2}}=374.77\widehat{i}+374.77\widehat{j}[/tex]
[tex]\overrightarrow{d_{3}}=480\left ( - Cos45\widehat{i}+Sin45\widehat{j} \right )[/tex]
[tex]\overrightarrow{d_{3}}=-339.41\widehat{i}+339.41widehat{j}[/tex]
The resultant displacement is given by
[tex]\overrightarrow{d}\overrightarrow{d_{1}}+\overrightarrow{d_{2}}+\overrightarrow{d_{3}}[/tex]
[tex]\overrightarrow{d}=\left ( 374.77-339.41 \right )\widehat{i}+\left ( 580+374.77+339.41 \right )\widehat{j}[/tex]
[tex]\overrightarrow{d}=35.36\widehat{i}+1294.18\widehat{j}[/tex]
magnitude of the displacement
[tex]d ={\sqrt{35.36^{2}+1294.18^{2}}}=1294.66 m[/tex]
d = 1294.66 m
(b) Let θ be the angle from + X axis direction in counter clockwise
[tex]tan\theta =\frac{1294.18}{35.36}=36.6[/tex]
θ = 88.44°