What is the Resultant Force on a Car with Two Differently Angled Forces?

[mike98020205]

Two forces are applied to a car in an effort to accelerate it. one is 450N and is applied noth of west at a 10 degree angle and the other is 380N, applied north of east at a 30 degree angle. What is the resultant of these two forces?
I attatched a file to provide a visual aid even though it's not a very good. I'm confused by the question it self. A resultant is a vector representing the sum of two or more vectors. For the problems I've been doing, that usually the hypotenuse of a right triangle. If you draw an imaginary line down and then right or left depending on which vector, it makes a right triangle. It appears to me that they are already resultants.

 

[whozum]

With vectors, you can move them around (as you are supposed to) to add them. Move one of the vectors so that its tail (butt) is in the other vectors head (arrow), and then draw your hypotenuse like that.

 

[quicknote]

I would approach this question by first identifying the given information and then using mathematical principles to determine the resultant of the two forces.

First, I would draw a diagram to visualize the situation. The two forces, 450N and 380N, are applied at different angles, 10 degrees and 30 degrees respectively. This means that the two forces are not acting in the same direction and will need to be combined to find the resultant force.

Next, I would use vector addition to determine the resultant force. This involves breaking down the two forces into their horizontal and vertical components and then adding them together. In this case, the horizontal component of the first force is 450N cos(10) and the vertical component is 450N sin(10). Similarly, the horizontal component of the second force is 380N cos(30) and the vertical component is 380N sin(30).

Once the components are determined, I would add the horizontal components together and the vertical components together. This would give me the resultant force in both the horizontal and vertical directions. Using the Pythagorean theorem, I would then find the magnitude of the resultant force by taking the square root of the sum of the squares of the horizontal and vertical components.

Finally, I would use trigonometric principles to find the direction of the resultant force. This can be done by taking the inverse tangent of the vertical component over the horizontal component.

In conclusion, the resultant of the two forces, 450N and 380N, applied at angles of 10 degrees and 30 degrees respectively, can be calculated using vector addition and trigonometric principles. The resultant force would have a magnitude of approximately 649.4N and a direction of approximately 23.4 degrees north of east.