A bird is attempting to fly northeast at a constant speed, but a wind blowing southward at 5 miles per hour blows the bird off course. If the bird’s overall movement (incorporating its intended movement

and the movement due to wind) is at a speed of √53 miles per hour, how fast would it have been traveling if there was no wind?

The value is

Step-by-step explanation:

From the question we are told that

The velocity of the wind southward is

The resultant velocity of the bird with the with wind is

Generally for an object moving in the northwest direction the angle with the horizontal is 45°

Generally the velocity of the bird in the along the x -axis is

Generally the velocity of the bird in the along the y -axis is

Here is the velocity of the bird without the wind

Generally the resultant velocity of the bird with the with wind is mathematically represented as

=>

Generally

and

So

=>

=>

=>

Solving the above quadratic equation using quadratic formula we obtain that

The other value is negative so we do not make use of it because we know that the bird is moving in the positive x and y axis