Answer:
Work Done = 27.66 Joules
Step-by-step explanation:
The work done is:
[tex]W=F*d*Cos \theta[/tex]
Where
F is the fore
d is the distance moved
[tex]\theta[/tex] is the angle
The force is "4"
The distance is the distance from (1,7) to (8,10)
The distance is the square root of change in y coordinates, squared and sum of change in x coordinates, squared. Hence, distance is:
[tex]\sqrt{(10-7)^2+(8-1)^2}\\=\sqrt{3^2+7^2}\\\sqrt{58}[/tex]
The angle is gotten by the formula:
[tex]Cos\phi = \frac{Force in x direction}{Distance}\\Cos\phi = \frac{8-1}{\sqrt{58}}\\Cos\phi=\frac{7}{\sqrt{58}}\\\phi = Cos^{-1}\frac{7}{\sqrt{58}}\\\phi = 23.21[/tex]
So, now:
[tex]\theta = 48 - 23.21 = 24.79[/tex]
Work Done = [tex]F*d * Cos\theta = 4 * \sqrt{58} * Cos(24.79)[/tex]
Work Done = 27.66 Joules
