Rebecca's car is stuck in the mud. Major and Amy come along...

Rebecca's car is stuck in the mud. Major and Amy come along in a truck to help pull her out. They attach one end of a tow strap to the front of the car and the other end to the truck's trailer hitch, and the truck starts to pull. Meanwhile, Major and Amy get behind the car and push. The truck generates a horizontal force of 336 lb on the car. Major and Amy are pushing at a slight upward angle and generate a force of 115 lb on the car. These forces can be represented by vectors, as shown in the figure below. The angle between these vectors is 10.9°. Find the resultant force (the vector sum), then give its magnitude and its direction angle from the positive x-axis. a. The resultant force is (Tip: omit degree notations from your answers; e.g. enter cos(45) instead of cos(45°)) b. It's magnitude is lb. c. It's angle from the positive x-axis is Hint: For a detailed solution, see the example (Finding Resultant Force) in Section 2.1 (Vectors in the Plane).

Transcript

00:01 For this question, they say that alma's car is stuck in the mud.

00:03 Ahmed and kyle come along in a truck to help pull her out.

00:07 They attach one end of a toe strap to the front of the car and the other end to the truck's trailer hitch.

00:13 And the truck starts to pull.

00:15 Meanwhile, ahmed and kyle get behind the car and push.

00:19 The truck generates a horizontal force of 336 pounds on the car.

00:25 Ahmed and kyle are pushing at a slight upward angle and generate a force.

00:30 Of 105 pounds on the car.

00:33 These forces can be represented as vectors as shown in the figure below.

00:37 The angle between these vectors is 24 .3 degrees.

00:41 I want to find the resultant force and then give its magnitude and direction from the positive x -axis.

00:48 So first we're going to get the resultant force.

00:52 So if i call this horizontal force, force 1, and this other force 2, i'm going to represent both of them as vectors.

01:03 I'm going to say that force 1 is 336 units in the positive x direction and no units in the y direction.

01:14 So that's my force 1.

01:16 Now how about my second force? well the first component you may remember that any vector can be written in the form of magnitude of v times the cosine of theta, comma magnitude of v times the sine of theta, where theta is the angle from the positive x -axis.

01:39 And so what do we have for force 2? well, it has components 105 times the cosine of 24 .3 degrees, comma, 105 times the 105 times the sign of 24 .3 degrees.

01:57 So if i wanted the resultant force f1 plus f2, what does that look like? while f1 plus f2, it's going to have components 336 plus 105 times the cosine of 24 .3 degrees in my first component, and 105 times the sign of 24 .3 degrees in the second component.

02:26 Now, they did say we can omit the degree notations from my answer, so i don't need that.

02:31 So i could just fill it in this way.

02:33 I could say i have 336 plus 105 times the cosine of 24 .3 degrees.

02:46 And then i have 105 times the sign of 24 .3 degrees.

02:54 Now, i'm going to want to know what the magnitude is...

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