Question

A bird flies at 20 m/s in still air is flying Northward while the wind blows Eastward at 15 m/s. Relative to the ground, the bird is flying at ________.

Answer 1

The bird's velocity relative to the ground is approximately 24.49 m/s at an angle of 37.5 degrees north of east.

Step-by-step explanation:

To find the bird's velocity relative to the ground, we need to consider its velocity relative to the air and the velocity of the wind. The bird's velocity relative to the ground is the vector sum of its velocity relative to the air and the velocity of the wind.

Given that the bird flies at 20 m/s in still air and the wind blows at 15 m/s Eastward, we can say that the bird's velocity relative to the air is 20 m/s northward. The velocity of the wind is 15 m/s eastward.

To calculate the bird's velocity relative to the ground, we can use vector addition. We add the bird's velocity relative to the air (20 m/s northward) and the velocity of the wind (15 m/s eastward).

The resultant velocity can be found using the Pythagorean theorem. The magnitude of the resultant velocity is given by the square root of the sum of the squares of the individual velocities. In this case, the magnitude of the resultant velocity is approximately 24.49 m/s. The direction can be found using trigonometry. The tangent of the angle between the resultant velocity and the eastward direction is given by the ratio of the bird's velocity relative to the air to the velocity of the wind. In this case, the angle is approximately 37.5 degrees north of east.