To solve this problem, we need to understand that the plane is moving in a direction that is a combination of two perpendicular directions: North and East. This forms a right triangle, where the plane's velocity is the hypotenuse, and the North and East components are the two legs of the triangle.

Given that the plane is moving Northeast, it means it's moving at a 45-degree angle. This implies that the North and East components of the velocity are equal. So, the Northern component of the velocity is also 300 m/h.

We can use the Pythagorean theorem to find the magnitude of the plane's velocity. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). In mathematical terms, this is expressed as:

c² = a² + b²

In this case, a and b are both 300 m/h. So we can substitute these values into the equation:

c² = (300 m/h)² + (300 m/h)²
c² = 90000 (m²/h²) + 90000 (m²/h²)
c² = 180000 (m²/h²)

To find c (the plane's velocity), we take the square root of both sides of the equation:

c = sqrt(180000) m/h
c = approximately 424.26 m/h

So, the plane is travelling at a speed of approximately 424.26 m/h.

Question

To solve this problem, we need to understand that the plane is moving in a direction that is a combination of two perpendicular directions: North and East. This forms a right triangle, where the plane's velocity is the hypotenuse, and the North and East components are the two legs of the triangle.

Given that the plane is moving Northeast, it means it's moving at a 45-degree angle. This implies that the North and East components of the velocity are equal. So, the Northern component of the velocity is also 300 m/h.

We can use the Pythagorean theorem to find the magnitude of the plane's velocity. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). In mathematical terms, this is expressed as:

c² = a² + b²

In this case, a and b are both 300 m/h. So we can substitute these values into the equation:

c² = (300 m/h)² + (300 m/h)²
c² = 90000 (m²/h²) + 90000 (m²/h²)
c² = 180000 (m²/h²)

To find c (the plane's velocity), we take the square root of both sides of the equation:

c = sqrt(180000) m/h
c = approximately 424.26 m/h

So, the plane is travelling at a speed of approximately 424.26 m/h.

Knowee AI · Accepted Answer

To solve this problem, we need to understand that the plane is moving in a direction that is a combination of two perpendicular directions: North and East. This forms a right triangle, where the plane's velocity is the hypotenuse, and the North and East components are the two legs of the triangle.

Given that the plane is moving Northeast, it means it's moving at a 45-degree angle. This implies that the North and East components of the velocity are equal. So, the Northern component of the velocity is also 300 m/h.

We can use the Pythagorean theorem to find the magnitude of the plane's velocity. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). In mathematical terms, this is expressed as:

c² = a² + b²

In this case, a and b are both 300 m/h. So we can substitute these values into the equation:

c² = (300 m/h)² + (300 m/h)²
c² = 90000 (m²/h²) + 90000 (m²/h²)
c² = 180000 (m²/h²)

To find c (the plane's velocity), we take the square root of both sides of the equation:

c = sqrt(180000) m/h
c = approximately 424.26 m/h

So, the plane is travelling at a speed of approximately 424.26 m/h.

A plane is travelling Northeast. If the eastern component of its velocity is 300 m/h, how fast is the plane travelling?

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