Question

Find the work done by a force F of 30 pounds acting in the direction in moving an object 3 feet from (0, 0) to a point in the first quadrant along the line

Answer 1

Step-by-step explanation:

Assumption: Supposing we have to find Force along the line
`y=(1)/(2)x` acting in the direction (2,2).

So, F in the direction (2,2)

`F=(30)/(√(2^2+2^2))=(30√(2))/(2)`

The object is moving from point 0,0 to x, x/2. a distance of 3 feet. So, we can find the translation vector.(We must take the positive root since, we are in first quadrant.

`x^2+(x^2)/(4)=3^2`

`\Rightarrow 5x^2=36`

`\Rightarrow x=(6)/(√(5))=(3(√(5)0)/(5)`

therefore,

Work done W = F.x

`=(90√(10))/(10)(1+2)=27√(10)`