what displacement must be added to a 50 cm displacement in the +x direction to give a resultant displacement of 85 cm at 25 degrees?
(i know the ans, just need to know how to get the ans)
Try to get.
Take the resultant, figure the vertical and hoizontal component of the resultant.
vertical 85sin25
horizontal 85 cos25
So the added displacement must supply
vertical 85 sin 25
horizontal 85 cos25 -50cm
use these components to get the displacement and angle.
I don't know it
To determine the displacement that must be added to a 50 cm displacement in the +x direction to achieve a resultant displacement of 85 cm at 25 degrees, we can break down the problem into its x and y components using trigonometry.
Step 1: Draw a vector diagram:
Start by drawing a coordinate system with the initial displacement and the resultant displacement. Label the initial displacement as vector A and the resultant displacement as vector R, as shown:
A (+x direction)
------>
|
|\
| \
| \
| \ R
| \
|
Step 2: Find the x-component of the resultant displacement:
Given that the resultant displacement is 85 cm at 25 degrees, we need to find the x-component of this displacement. We can use trigonometry to do this.
The x-component (Rx) of the resultant displacement can be found using the cosine function:
Rx = R * cos(θ)
where R is the magnitude of the resultant displacement and θ is the angle it makes with the positive x-axis.
In this case, R = 85 cm and θ = 25 degrees. Converting the angle to radians, we have:
θ = 25° * (π/180°) = 25π/180 radians
Substituting these values into the equation, we can find Rx.
Step 3: Find the x-component of the initial displacement:
The initial displacement is given as 50 cm in the +x direction. Since it is purely in the x-direction, the x-component of the initial displacement (Ax) is simply 50 cm.
Step 4: Determine the additional displacement needed:
The displacement to be added to the initial displacement to achieve the resultant displacement is essentially the difference between the x-components of the resultant displacement and initial displacement. In other words:
Additional displacement needed = Rx - Ax
Substituting the values we found earlier, we can calculate the additional displacement needed.
Using this step-by-step approach, you should arrive at the answer for the additional displacement needed to achieve the resultant displacement of 85 cm at 25 degrees in the +x direction.