High School

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A particle undergoes two displacements. The first has a magnitude of 163 cm and makes an angle of 128° with the positive x-axis. The resultant displacement has a magnitude of 176 cm and is directed at an angle of 36.8° to the positive x-axis. Find the magnitude of the second displacement.

Answer in units of cm.

Answer :

Answer:

[tex]d_2 = 242.44 cm[/tex]

Explanation:

First displacement is given as

[tex]d_1[/tex] = 163 cm at 128 degree

so we have

[tex]d_1 = 163 cos128 \hat i + 163 sin128 \hat j[/tex]

[tex]d_1 = -100.35 \hat i + 128.4 \hat j[/tex]

Now the resultant displacement is given as

[tex]d[/tex] = 176 cm at 36.8 degree

so we have

[tex]d = 176 cos36.8 \hat i + 176 sin36.8 \hat j[/tex]

[tex]d = 141 \hat i + 105.4 \hat j[/tex]

now we know that

[tex]d = d_1 + d_2[/tex]

[tex]141 \hat i + 105.4\hat j = -100.35 \hat i + 128.4 \hat j + d_2[/tex]

[tex]d_2 = 141\hat i + 105.4\hat j + 100.35 \hat i - 128.4 \hat j[/tex]

[tex]d_2 = 241.35 \hat i - 23\hat j[/tex]

so magnitude of the above displacement is given as

[tex]d_2 = \sqrt{241.35^2 + 23^2}[/tex]

[tex]d_2 = 242.44 cm[/tex]

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