A particle undergoes two displacements. The first has a magnitude of 135cm and makes an angle of 114° with the positive x axis. The resultant displacement had a magnitude of 183cm and is directed at an angle of 21.8° to the positive x axis. Find the magnitude of the second displacement. Answer in units of cm

To find the magnitude of the second displacement, we can use vector addition. Let's break down the given information:

First displacement: magnitude = 135 cm, angle = 114° with the positive x-axis.
Resultant displacement: magnitude = 183 cm, angle = 21.8° with the positive x-axis.

We can represent the first displacement as a vector using its components in the x and y directions. Let's call this vector A:
Ax = 135 cos(114°)
Ay = 135 sin(114°)

Now let's represent the resultant displacement as a vector using its components in the x and y directions. Let's call this vector R:
Rx = 183 cos(21.8°)
Ry = 183 sin(21.8°)

To find the magnitude of the second displacement, we can use the vector addition formula:

R = A + B

Where B is the second displacement vector.

Since the magnitudes of R, A, and B are given, we can write:

|A| + |B| = |R|

Substituting the given values:

135 + |B| = 183

Simplifying the equation:

|B| = 183 - 135
|B| = 48 cm

Therefore, the magnitude of the second displacement is 48 cm.

To find the magnitude of the second displacement, we can use vector addition.

First, let's represent the first displacement as vector A and the second displacement as vector B.

Vector A has a magnitude of 135 cm and makes an angle of 114° with the positive x-axis. We can break down vector A into its horizontal and vertical components.

The horizontal component (Ax) of vector A can be found using the cosine function:
Ax = 135 cm * cos(114°)

The vertical component (Ay) of vector A can be found using the sine function:
Ay = 135 cm * sin(114°)

Next, let's represent the resultant displacement as vector R.
Vector R has a magnitude of 183 cm and makes an angle of 21.8° with the positive x-axis.

We can also break down vector R into its horizontal and vertical components.

The horizontal component (Rx) of vector R can be found using the cosine function:
Rx = 183 cm * cos(21.8°)

The vertical component (Ry) of vector R can be found using the sine function:
Ry = 183 cm * sin(21.8°)

Now, we can use vector addition. The sum of the horizontal components should equal the horizontal component of the resultant, and the sum of the vertical components should equal the vertical component of the resultant.

Ax + Bx = Rx
Ay + By = Ry

Since we're looking for the magnitude of vector B, let's isolate Bx and By:

Bx = Rx - Ax
By = Ry - Ay

Finally, we can find the magnitude of vector B using the Pythagorean theorem:

Magnitude of B = sqrt(Bx^2 + By^2)

Plug in the values we've calculated and solve for the magnitude of B.