Question

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

Answer 1

magnitude of the force is

`F = 1537 N`

direction of the force is given as

`\theta = 25.3 degree`

Step-by-step explanation:

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

so we have

`F_1 = 598(cos29 \hat i + sin29 \hat j)`

`F_1 = 523 \hat i + 290 \hat j`

Now another force is 941 N at 23 degree

`F_2 = 941(cos23\hat i + sin23\hat j)`

`F_2 = 866.2 \hat i + 367.7 \hat j`

so we will have

`F = F_1 + F_2`

`F = (523 + 866.2)\hat i + (290 + 367.7)\hat j`

`F = 1389.2\hat i + 657.7 \hat j`

magnitude of the force is

`F = √(1389.2^2 + 657.7^2)`

`F = 1537 N`

direction of the force is given as

`tan\theta = (F_y)/(F_x)`

`tan\theta = (657.7)/(1389.2)`

`\theta = 25.3 degree`