force 15i -16j N is added to another 23i N. In what direct measured from the positive x-axis does the resultant act?
adding vectors ... 15i + 7j
the tangent of the direction angle is
... tan(Θ) = 7/15
Well, well, well, looks like we've got some vectors getting together for a party! So, let's see what they're up to. We have a force of 15i - 16j N hanging out and another force of 23i N joining the party. Now, to find where the resultant force is acting from the positive x-axis, we need to do a little math.
First, let's add these vectors together. When we add 15i - 16j N and 23i N, we get a resultant force of 38i - 16j N.
Now, we want to measure the direction of this resultant force from the positive x-axis. To do that, we can use a little trigonometry. We'll take the inverse tangent of the y-component divided by the x-component of our resultant force.
So, the direction from the positive x-axis that the resultant force acts can be found using the equation:
θ = arctan(y-component / x-component)
In this case, the y-component is -16j and the x-component is 38i. Let's plug those numbers in and see what we get.
θ = arctan(-16 / 38)
Now, I could give you the exact value using a calculator, but let's not get too serious. How about we round it up? The resultant force acts at an angle of approximately 24.69 degrees from the positive x-axis.
And there you have it! The party animals, or should I say vectors, are having a blast at an angle of about 24.69 degrees from the positive x-axis. Let's hope they don't get too carried away!
To find the direction of the resultant force, we need to calculate the angle it makes with the positive x-axis.
First, let's find the magnitude of the resultant force. The magnitude of a vector can be calculated using the Pythagorean theorem:
Resultant Force = √[(15i)^2 + (-16j)^2]
Resultant Force = √[225 + 256]
Resultant Force = √481
Resultant Force ≈ 21.93 N
Next, let's calculate the angle θ that the resultant force makes with the x-axis using trigonometry:
θ = arctan((-16j) / 15i)
θ = arctan(-16/15)
θ ≈ -46.81 degrees
Since the trigonometric function arctan is negative in the second quadrant, the angle is negative. However, we can convert it to a positive angle by adding 180 degrees. Therefore, the angle that the resultant force makes with the positive x-axis is approximately:
θ = -46.81 + 180
θ ≈ 133.19 degrees
So, the resultant force acts at an angle of approximately 133.19 degrees from the positive x-axis.
To find the direction in which the resultant force acts, we can use vector addition.
Given:
Force 1 (15i - 16j) N
Force 2 (23i) N
Step 1: Add the two forces to find the resultant force.
To add the forces, we simply add the corresponding components of the vectors.
Resultant force = Force 1 + Force 2
= (15i - 16j) N + (23i) N
= (15i + 23i) N - 16j N
= 38i N - 16j N
So, the resultant force is (38i - 16j) N.
Step 2: Find the angle of the resultant force.
To find the angle of the resultant force with respect to the positive x-axis, we can use the tangent function.
Angle = atan(-16/38)
Using a scientific calculator or the trigonometric function in a programming language, calculate the arctangent of -16/38.
Angle ≈ -22.6094 degrees
Since this angle is negative, we add 180 degrees to obtain the angle measured from the positive x-axis.
Angle measured from the positive x-axis ≈ -22.6094 + 180 ≈ 157.3906 degrees
So, the resultant force acts at an angle of approximately 157.39 degrees measured from the positive x-axis.