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love history [14]
3 years ago
12

hegelich A particle undergoes two displacements. The first has a magnitude of 163 cm and makes an angle of 128 ◦ with the positi

ve 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
Physics
1 answer:
nata0808 [166]3 years ago
4 0

Answer:

d_2 = 242.44 cm

Explanation:

First displacement is given as

d_1 = 163 cm at 128 degree

so we have

d_1 = 163 cos128 \hat i + 163 sin128 \hat j

d_1 = -100.35 \hat i + 128.4 \hat j

Now the resultant displacement is given as

d = 176 cm at 36.8 degree

so we have

d = 176 cos36.8 \hat i + 176 sin36.8 \hat j

d = 141 \hat i + 105.4 \hat j

now we know that

d = d_1 + d_2

141 \hat i + 105.4\hat j = -100.35 \hat i + 128.4 \hat j + d_2

d_2 = 141\hat i + 105.4\hat j + 100.35 \hat i - 128.4 \hat j

d_2 = 241.35 \hat i - 23\hat j

so magnitude of the above displacement is given as

d_2 = \sqrt{241.35^2 + 23^2}

d_2 = 242.44 cm

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