Calculating the resultant force using vector

[SumDumKid]

Please HELP!

I need help with a question...I don't know how to do it...can someone please tell me how.
This question is about calculating the resultant force using vectors.

Question:
There is a parachutist with a 500 N force acting upwards on him and a 1000 N force acting downwards on him. There is also a 300 N force of wind acting towards him at a 45 degree angle. How do I calculate the resultant force on the parachutist?

thank you for your time

 

[Ronka]

So you have:

Forces in Y:
500N, 1000N

The force that act at a certain degree should be expressed in Y and X components:
If the wind of 300 N comes from below at 45 degree angle:

X component of the 300 N force: 300 x cos (45) = xxx N
Y component of the 300 N force: 300 x sin (45) = xxx N


to calculate the resultants of all forces use pythagoras

 

[ogb p]

To calculate the resultant force on the parachutist, we need to use vector addition. First, we need to break down the forces into their horizontal and vertical components. The 500 N upward force can be represented as (0, 500) while the 1000 N downward force can be represented as (0, -1000). The 300 N wind force at a 45 degree angle can be broken down into its horizontal and vertical components using trigonometry. The horizontal component will be 300*cos(45) = 212.1 N and the vertical component will be 300*sin(45) = 212.1 N.

Next, we can add all the horizontal and vertical components separately. The resultant horizontal force will be 0 + 0 + 212.1 = 212.1 N and the resultant vertical force will be 500 - 1000 + 212.1 = -287.9 N.

Finally, we can use the Pythagorean theorem to calculate the magnitude of the resultant force, which will be the square root of the sum of the squares of the horizontal and vertical components. In this case, the resultant force will be √(212.1^2 + (-287.9)^2) = 358.8 N.

To find the direction of the resultant force, we can use inverse tangent to calculate the angle. The angle will be tan^-1(-287.9/212.1) = -51.8 degrees. This means that the resultant force is acting at an angle of 51.8 degrees downwards from the horizontal.

Therefore, the resultant force on the parachutist is 358.8 N at an angle of 51.8 degrees downwards from the horizontal. I hope this helps with your question.