Question

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 ◦ .

Answer 1

`\theta = 211.7 degree`

Step-by-step explanation:

First displacement of the particle is given as

`r_1` = 11 m at 82 degree with positive X axis

so we can say

`\vec r_1 = 11 cos82 \hat i + 11 sin82 \hat j`

`\vec r_1 = 1.53\hat i + 10.9 \hat j`

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

`r = 8.7 cos135\hat i + 8.7 sin135\hat j`

`r = -6.15 \hat i + 6.15 \hat j`

now we know that

`r = r_1 + r_2`

now we have

`r_2 = r - r_1`

so we will have

`r_2 = (-6.15 \hat i + 6.15 \hat j) - (1.53\hat i + 10.9 \hat j)`

`r_2 = -7.68 \hat i - 4.75 \hat j`

so angle of the second displacement is given as

`tan\theta = (r_y)/(r_x)`

`tan\theta = (-4.75)/(-7.68)`

`\theta = 211.7 degree`