First, draw a diagram of the given information. We can label the angle of inclination as , but furthermore, in this type of problem, the angle formed between and is equal to that same measure, so that has also been labelled . Because these two angles are equal, and (see second diagram).

Using the above formulas, we get:

lbs

lbs

Next understand that the minimum force needed to prevent the barrel from rolling down the plane corresponds to , so the minimum force to prevent the barrel from rolling is lbs. The force against the inclined plan is lbs. Finally, because , the barrel will not roll down the inclined plane.

First, draw a diagram of the given information. We can label the angle of inclination as , but furthermore, in this type of problem, the angle formed between and is equal to that same measure, so that has also been labelled . Because these two angles are equal, and (see second diagram).

Using the above formulas, we get:

lbs

lbs

Next understand that the minimum force needed to prevent the barrel from rolling down the plane corresponds to , so the minimum force to prevent the barrel from rolling is lbs. The force against the inclined plan is lbs. Finally, because , the barrel will not roll down the inclined plane.

To find the resultant we must sum the two vectors:

Now we must graph the resultant

To find the resultant we must sum the two vectors:

Now we must graph the resultant

We can use the pythagorean theorem to solve this problem. Using as our hypotenuse, we can drop a vertical vector perpendicular to the x-axis. We will call this and it is 4 units in length. We can also extend a vector from the origin that connects to . We will call this and it is 3 units in length.

Using the pythagorean theorem:

We can use the pythagorean theorem to solve this problem. Using as our hypotenuse, we can drop a vertical vector perpendicular to the x-axis. We will call this and it is 4 units in length. We can also extend a vector from the origin that connects to . We will call this and it is 3 units in length.

Using the pythagorean theorem:

When determining the resultant of two vectors, you are finding the sum of two vectors. To do this you must add the x component and the y component separately.

When determining the resultant of two vectors, you are finding the sum of two vectors. To do this you must add the x component and the y component separately.

The bearing of a point B from a point A in a horizontal plane is defined as the acute angle made by the ray drawn from A through B with the north-south line through A. The bearing is read from the north or south line toward the east or west. Bearing is typically only represented in degrees (or degrees and minutes) rather than radians. To find , start in the south direction, then move towards the west:

The other incorrect answer choices provided depict , , and .

This question and its answer choices give you a few clues to work with. First, we need to identify the bearing angle being shown. The options in the answer choices are either , , or . Because the angle begins in the south direction and moves towards the west, the correct bearing is . That means only two of the answer choices could be correct. We now need to understand how the miles per hour corresponds to the problem. Notice that there is no answer choice that has the bearing of and velocity of miles per hour. Rather, we need to choose between miles per hour for hours or miles per hour for hours. Because miles per hour for hours corresponds to (whereas the other option corresponds to only ), the correct answer is "A motorboat traveling at miles per hour for hours."