Find the resultant of the following two displacements; 2.0 m 40 degrees 4.0 meters at 127 degrees. the angles are taken relative to the x-axis
To find the resultant of two displacements, we can use vector addition.
Let's break down the given displacements into their components along the x-axis and the y-axis:
Displacement 1:
Magnitude = 2.0 m
Direction = 40 degrees
We can find the x-component of Displacement 1 by using the cosine function:
x1 = 2.0 m * cos(40 degrees) ≈ 1.528 m
And we can find the y-component of Displacement 1 by using the sine function:
y1 = 2.0 m * sin(40 degrees) ≈ 1.295 m
Similarly, for Displacement 2:
Magnitude = 4.0 m
Direction = 127 degrees
x2 = 4.0 m * cos(127 degrees) ≈ -0.868 m
y2 = 4.0 m * sin(127 degrees) ≈ 3.425 m
Now, we can add the x-components of both displacements to get the overall x-component:
x_resultant = x1 + x2 ≈ 1.528 m - 0.868 m ≈ 0.66 m
And we can add the y-components of both displacements to get the overall y-component:
y_resultant = y1 + y2 ≈ 1.295 m + 3.425 m ≈ 4.72 m
Now, we can find the magnitude of the resultant displacement using the Pythagorean theorem:
Resultant magnitude = √(x_resultant^2 + y_resultant^2)
= √(0.66 m^2 + 4.72 m^2)
≈ 4.77 m
To find the angle of the resultant displacement, we can use the inverse tangent function:
Resultant direction = arctan(y_resultant / x_resultant)
= arctan(4.72 m / 0.66 m)
≈ 84.5 degrees
Therefore, the resultant of the two displacements is approximately 4.77 m at an angle of 84.5 degrees relative to the x-axis.
x = 2 cos 40 + 4 cos 127
y = 2 sin 40 + 4 sin 127
magnitude^2 = x^2+y^2
tan angle to x axis = y/x