Question

A pair of tow trucks are pulling on a trailer that is stuck

in mud. The first truck pulls a a pair of tow trucks are pulling on a trailer that is stuck in mud. the first truck pulls with a force of 10,000

pounds at a 110° angle from the second truck, which is

pulling with a force of 7,500 pounds. What is the

magnitude of the resultant force?

9.821 pounds

10,244 pounds

14,405 pounds

24 226 pounds

Answer 1

Answer:b

Explanation:

Took the test

Answer 2

R=10,244 Lb

Explanation:

In order to solve this problem, we can start by drawing the situation. (See attached picture).

We can look at the forces applied by the trucks as vectors, so in this case, in order to find the resultant force, we can add the two vectors. You can do so by drawing one force after the other and join the start of the first force with the end of the second force to form a triangle. The missing side will be the resultant force. In that triangle I drew there, the inner angle will be found by subtracting 180°-110°=70°

In this case we can find the resultant force by using the law of cosines:

`A^(2)=B^(2)+C^(2)-2AB cos \alpha`

so we can use the data given by the problem:

`R^(2)=T_(1)^(2)+T_(2)^(2)-2T_(1)T_(2) cos \alpha`

so we can solve this for R, so we get:

`R=\sqrt{T_(1)^(2)+T_(2)^(2)-2T_(1)T_(2) cos \alpha}`

now we can substitute:

`R=\sqrt{(10,000Lb)^(2)+(7,500Lb)^(2)-2(10,000Lb)(7,500Lb) cos (70^(0))}`

which yields:

R=10,244Lb