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Two men decide to use their cars to pull a truck stuck in mud. They attach ropes and one pulls with a force of 598 N at an angle of 29◦ with respect to the direction in which the truck is headed, while the other car pulls with a force of 941 N at an angle of 23◦ with respect to the same direction. 598 N 29 ◦ 941 N 23 ◦ What is the net forward force exerted on the truck in the direction it is headed? Answer in units of N

Respuesta :

Answer:

magnitude of the force is

[tex]F = 1537 N[/tex]

direction of the force is given as

[tex]\theta = 25.3 degree[/tex]

Explanation:

As we know that the first force is 598 N at 29 degree

so we have

[tex]F_1 = 598(cos29 \hat i + sin29 \hat j)[/tex]

[tex]F_1 = 523 \hat i + 290 \hat j[/tex]

Now another force is 941 N at 23 degree

[tex]F_2 = 941(cos23\hat i + sin23\hat j)[/tex]

[tex]F_2 = 866.2 \hat i + 367.7 \hat j[/tex]

so we will have

[tex]F = F_1 + F_2[/tex]

[tex]F = (523 + 866.2)\hat i + (290 + 367.7)\hat j[/tex]

[tex]F = 1389.2\hat i + 657.7 \hat j[/tex]

magnitude of the force is

[tex]F = \sqrt{1389.2^2 + 657.7^2}[/tex]

[tex]F = 1537 N[/tex]

direction of the force is given as

[tex]tan\theta = \frac{F_y}{F_x}[/tex]

[tex]tan\theta = \frac{657.7}{1389.2}[/tex]

[tex]\theta = 25.3 degree[/tex]

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