A flock of ducks is trying to migrate south for the winter, but they keep being blown off course by a wind blowing from the west at 11{\rm m/s} . A wise elder duck finally realizes that the solution is to fly at an angle to the wind.If the ducks can fly at 17{\rm m/s} relative to the air, in what direction should they head in order to move directly south?

To determine the direction the ducks should head in order to move directly south, we need to consider the vector components of their motion. Let's break it down step by step:

1. Start by drawing a diagram to visualize the problem. Draw a coordinate system with the north direction pointing up and the east direction pointing to the right.

2. We know that the wind is blowing from the west at 11 m/s. This means the wind velocity vector has a magnitude of 11 m/s and is pointing directly to the east (opposite to the wind's direction).

3. The ducks can fly at 17 m/s relative to the air. Let's call this velocity vector of the ducks "V_duck." Since we want to move directly south, the magnitude of V_duck should be equal to their desired speed, which is 17 m/s.

4. Now, let's analyze the duck's motion relative to the ground. The ground is stationary, so the motion of the ducks relative to the ground is the vector sum of the wind's motion and the duck's motion relative to the air.

5. We can find the resultant vector by adding the vectors representing the wind velocity and the duck's velocity. Draw the vectors according to their magnitudes and directions.

6. To add vectors, place the tail of one vector against the head of the other vector. Draw the resultant vector starting from the tail of the first vector to the head of the last vector.

7. Since we are looking for the direction in which the ducks should head, draw a line from the tail of V_duck to the head of the resultant vector.

8. Measure the angle between the resultant vector and the north direction on the diagram.

9. Use the trigonometric function tangent to find the angle. For a right triangle formed between the north direction, the resultant vector, and the east direction, the tangent of the angle is the ratio of the length of the horizontal side to the length of the vertical side.

10. Take the inverse tangent (arctan) of the tangent value calculated in step 9 to find the angle itself.

The angle you find will be the direction in which the ducks should head to move directly south against the wind.

At the instant the traffic light turns green, an automobile that has been waiting at an intersection starts ahead with a constant acceleration of 2.80{\rm m}/{\rm s}^{2} . At the same instant, a truck, traveling with a constant speed of 14.8{\rm m}/{\rm s} , overtakes and passes the automobile.