Respuesta :
Answer:
18.3 m , 25.4°
Explanation:
d1 = 6 m, θ1 = 40°
d2 = 8 m, θ2 = 30°
d3 = 5 m, θ3 = 0°
Write the displacements in the vector form
[tex]d_{1}=6\left ( Cos40\widehat{i}+Sin40\widehat{j} \right )=4.6\widehat{i}+3.86\widehat{j}[/tex]
[tex]d_{2}=8\left ( Cos30\widehat{i}+Sin30\widehat{j} \right )=6.93\widehat{i}+4\widehat{j}[/tex]
[tex]d_{3}=5\widehat{i}[/tex]
The total displacement is given by
[tex]\overrightarrow{d}=\overrightarrow{d_{1}}+\overrightarrow{d_{2}}+\overrightarrow{d_{3}}[/tex]
[tex]d=\left ( 4.6+6.93+5 \right )\widehat{i}+\left ( 3.86+4 \right )\widehat{j}[/tex]
[tex]d=16.53\widehat{i}+7.86\widehat{j}[/tex]
magnitude of resultant displacement is given by
[tex]d ={\sqrt{16.53^{2}+7.86^{2}}}=18.3 m[/tex]
d = 18.3 m
Let θ be the angle of resultant displacement with + x axis
[tex]tan\theta =\frac{7.86}{16.53}=0.4755[/tex]
θ = 25.4°
