A particle undergoes two displaments , measured from the positive x-axis, with counterclockwise positive.The first has a magnitude of 11 m and makes an angle of 88 with the positive x-axis. The resultant displacement has a magnitude of 6.8 m direceted at an angle of 115 from the positive x-axis.

Find the magnitude of the second displacement. Find the angle of the second displacement (measured from the positive x axis, with counterclockwise positive within the limits of -180 to +180)

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

First, let's break down the first displacement into its x and y components. The magnitude of the first displacement is given as 11 m, and the angle it makes with the positive x-axis is 88°.

To find the x-component (horizontal component), we can use the cosine function:
x-component = 11 m * cos(88°)

To find the y-component (vertical component), we can use the sine function:
y-component = 11 m * sin(88°)

Now, let's move on to the second displacement. The resultant displacement has a magnitude of 6.8 m and an angle of 115° with the positive x-axis.

Again, we can break this displacement into its x and y components. To find the x-component, we use the cosine function:
x-component = 6.8 m * cos(115°)

To find the y-component, we use the sine function:
y-component = 6.8 m * sin(115°)

Now, we can find the total x and y components by summing up the respective components of the first and second displacements:

Total x-component = first x-component + second x-component
Total y-component = first y-component + second y-component

We know the total x-component (resultant x-component) and total y-component (resultant y-component) from the given information.

To find the magnitude of the second displacement, we use the Pythagorean theorem:
Magnitude of second displacement = sqrt[(total x-component)^2 + (total y-component)^2]

To find the angle of the second displacement (measured from the positive x-axis with counterclockwise positive within the limits of -180° to +180°), we use the inverse tangent function:
Angle = atan2(total y-component, total x-component)

Now that we have all the components, simply plug in the values and solve the equations to find the magnitude and angle of the second displacement.

Just convert the data to rectangular coordinates:

11 @ 88° = 0.0349,10.9933
6.8 @ 115V = -2.8738,6.1629

so, now you want (x,y) such that

0.0349+x = -2.8738
10.9933+y = 6.1629

Then convert that (x,y) back to polar avlues.