Question

hegelich 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 1

`d_2 = 242.44 cm`

Step-by-step 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 = √(241.35^2 + 23^2)`

`d_2 = 242.44 cm`