What displacement must be added to a 50 cm displacement in the +x-direction to give a resultant displacement
of 85 cm at 25°?
well in the x direction it is 85 cos 25 - 50
and in the y direction it is 85 sin 25
50 + D = 85[25o].
D = 85[25] - 50 = 77+35.9i - 50 = 27 + 35.9i = 44.9cm[53.1o] = Displacement added.
Steps are not show properly
To find the displacement that must be added to a given displacement to give a resultant displacement, we can use vector addition. Here's how to do it:
1. Convert the given displacements into vector form. The 50 cm displacement in the +x-direction can be written as (50, 0) cm, while the resultant displacement can be written as (85 cos 25°, 85 sin 25°) cm.
2. Add the two vectors together. In vector form, the addition is done component-wise. So, add the x-components together and add the y-components together. The resulting vector will be the displacement that must be added to the initial displacement to get the resultant displacement.
(50 + 85 cos 25°, 0 + 85 sin 25°) cm
3. Compute the components of the resultant vector. Use the sum of angles formula to calculate the x and y components:
x-component = 50 + 85 cos 25°
y-component = 0 + 85 sin 25°
4. Calculate the magnitudes of the components. The magnitude of the resultant displacement can be found using the Pythagorean theorem:
magnitude = √(x-component^2 + y-component^2)
Calculate the square of the x-component, the square of the y-component, sum them, and take the square root of the result.
magnitude = √((50 + 85 cos 25°)^2 + (85 sin 25°)^2) cm
5. The displacement that must be added to the initial displacement to give the resultant displacement is then given by the x and y components calculated in step 3.