A particle undergoes two displacements. The first has a magnitude of 11 m and makes an angle of 82 ◦ with the positive x axis. The result after the second displacement is 8.7 m directed at an angle of 135◦ to the positive x axis using counterclockwise as the positive angular direction schoenzeit (ms83473) – Assignment 01-1 – pusch – (19512020) 5 135◦ 82◦ 11 m 8.7 m Find the angle of the second displacement measured counterclockwise from the positive x axis (i.e., a positive angle). Answer in units of ◦ .

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aristocles aristocles · Answer 1 · 2019-09-20T02:59:27+02:00

Answer:

[tex]\theta = 211.7 degree[/tex]

Explanation:

First displacement of the particle is given as

[tex]r_1[/tex] = 11 m at 82 degree with positive X axis

so we can say

[tex]\vec r_1 = 11 cos82 \hat i + 11 sin82 \hat j[/tex]

[tex]\vec r_1 = 1.53\hat i + 10.9 \hat j[/tex]

resultant displacement of the particle after second displacement is given as

r = 8.7 m at 135 degree with positive X axis

so we can say

[tex]r = 8.7 cos135\hat i + 8.7 sin135\hat j[/tex]

[tex]r = -6.15 \hat i + 6.15 \hat j[/tex]

now we know that

[tex]r = r_1 + r_2[/tex]

now we have

[tex]r_2 = r - r_1[/tex]

so we will have

[tex]r_2 = (-6.15 \hat i + 6.15 \hat j) - (1.53\hat i + 10.9 \hat j)[/tex]

[tex]r_2 = -7.68 \hat i - 4.75 \hat j[/tex]

so angle of the second displacement is given as

[tex]tan\theta = \frac{r_y}{r_x}[/tex]

[tex]tan\theta = \frac{-4.75}{-7.68}[/tex]

[tex]\theta = 211.7 degree[/tex]