What displacement must be added to a 50cm displacement in the +x-direction to give a resultant displacement of 85cm at 25 degrees
85cm @ 25 deg.
Convert the vector to hor. and ver
components.
x = hor = 85cos25 = 77 cm.
y = ver = 65*sin85 = 35.2 cm.
Additions to the vector:
x + 50 = 77,
x = hor = 77 - 50 = 27 cm to be added.
y + 0 = 35.2,
y = 35.2.
R = 27 + 35.2i = 44.4 @ 52.5 deg.
CORRECTIONS:
Y = ver = 85*sin25 = 35.2.
50i+xi=77i+36j
Xi=27i+36j
X=(27²+36²)½
X=45cm.
@ tan- I(36/27)=52°
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Well, if you want to give a resultant displacement of 85 cm at 25 degrees, you'd have to ask the displacement nicely and hope it agrees to go along with your plans. However, if it's being stubborn, you might need to use a little bit of trickery. So, my suggestion is to approach the 50 cm displacement and tell it, "Hey buddy, I know you want to go in the +x-direction, but how about we try a little detour? Let's go at a 25-degree angle and see what happens!" Add some popcorn for extra persuasion. Who knows, that might just do the trick and give you the desired resultant displacement. Good luck!
To find the displacement that must be added to a 50cm displacement in the +x-direction to give a resultant displacement of 85cm at an angle of 25 degrees, we can use vector addition.
Step 1: Represent the given displacements as vectors
The initial displacement of 50cm in the +x-direction can be represented as a vector: D1 = 50cm, 0 degrees (x-component: 50cm, y-component: 0cm)
The final resultant displacement of 85cm at 25 degrees can also be represented as a vector: R = 85cm, 25 degrees (x-component: 85cos(25), y-component: 85sin(25))
Step 2: Decompose the resultant vector into its x and y components
To apply the principle of vector addition, we need to decompose the resultant vector R into its x-component and y-component.
Rx = 85cm * cos(25) ≈ 76.781cm
Ry = 85cm * sin(25) ≈ 35.519cm
Step 3: Subtract the x-components of the two vectors
Since we want to find the displacement that must be added in the +x direction, we need to find the difference between the x-components of the two vectors.
Dx = Rx - D1x
Dx = 76.781cm - 50cm
Dx ≈ 26.781cm
Therefore, the displacement that must be added to the 50cm displacement in the +x-direction to give a resultant displacement of 85cm at 25 degrees is approximately 26.781cm in the +x-direction.