Question

A boat is heading across a lake in the direction of 35° (clockwise from north) propelled by a force of 750 lbs. A wind blowing from the direction 320° exerts a force of 150 lbs.

a. In what direction is the boat moving (nearest whole degree)?

b. What is the effective force in this direction?

Answer 1

The boat is moving approximately 9 degrees north of east with an effective force of 767 lbs.

Step-by-step explanation:

To determine the direction in which the boat is moving, we can find the resultant force by adding the force of the boat and the force of the wind.

If we draw a vector diagram, we can see that the boat will be moving in a direction that is between the direction of the boat's force and the wind force. Using trigonometry, we can calculate that the boat is moving in a direction approximately 9 degrees north of east.

The effective force in this direction can be found by using the Pythagorean theorem to calculate the magnitude of the resultant force. The magnitude of the boat's force is 750 lbs and the magnitude of the wind force is 150 lbs. Therefore, the magnitude of the resultant force is approximately 767 lbs.