what is the northward and eastward components of a 550 kph velocity of an airplane going NE?
cos 45 = sin 45 so both are
550 cos 45 = 550 (sqrt 2)/2
Well, well, well, we have an airplane ready to take on some trigonometry! Now, if your airplane is moving Northeast at a speed of 550 kph, we can break down its velocity into its northward and eastward components.
To get the northward component, we need to take into account that Northeast is 45 degrees between North and East. Now, remember your trig functions? Cosine is our friend here! To find the northward component, we just need to multiply the velocity by the cosine of 45 degrees.
So, the northward component is 550 kph × cos(45°). Don't worry, my friend, I won't leave you hanging there. The cosine of 45 degrees equals √2/2, which simplifies things nicely.
So, the northward component of our airplane's velocity is 550 kph × √2/2. Who said airplanes don't fly with a little bit of math in their wings, huh?
Now, for the eastward component, we need to use the same approach. We multiply the velocity by the sine of 45 degrees because sine loves the angle between North and East. Simplifying all the way, the eastward component is 550 kph × √2/2 as well.
Hope that helps you navigate the skies with a few laughs! Just remember, you'll always have a clown-bot sidekick to lighten the load of those complex math problems. Safe travels, my friend! 🤡✈️
To find the northward and eastward components of a velocity vector, we can use trigonometry.
The velocity of the airplane going in a northeast direction can be divided into two components: one component is in the northward direction, and the other component is in the eastward direction.
Since the airplane is going at 550 kph, this is the magnitude of the velocity vector.
To find the components, we can use the trigonometric relationships between angles and sides of a right triangle.
In this case, the velocity vector forms a right triangle with the northward and eastward components being the legs of the triangle, and the magnitude of the velocity vector being the hypotenuse.
Since the airplane is going in a northeast direction, the angle between the northward component and the velocity vector is 45 degrees.
To find the northward component, we can use the cosine function, as follows:
Northward component = Velocity * cos(angle)
Northward component = 550 kph * cos(45°)
Northward component ≈ 550 kph * 0.7071
Northward component ≈ 388.9 kph
Similarly, to find the eastward component, we can use the sine function, as follows:
Eastward component = Velocity * sin(angle)
Eastward component = 550 kph * sin(45°)
Eastward component ≈ 550 kph * 0.7071
Eastward component ≈ 388.9 kph
Therefore, the northward and eastward components of the 550 kph velocity of the airplane going northeast are approximately 388.9 kph each.
To find the northward and eastward components of a velocity vector, such as an airplane traveling in a specific direction, you can use trigonometric functions and basic vector operations.
Since the airplane is moving in the northeast (NE) direction, the angle it forms with the north direction is 45 degrees (since NE is halfway between north and east). Taking this into account, we can use the following steps to calculate the northward and eastward components:
1. Start by finding the total velocity vector of the airplane. In this case, the magnitude (speed) of the velocity is given as 550 kph.
2. Use trigonometry to determine the northward component. Since it forms a right angle with the eastward direction, you can use the cosine function. The northward component can be found using the formula: Northward Component = Magnitude of Velocity * cosine(angle with north).
In this case, the northward component = 550 kph * cos(45 degrees).
3. Use trigonometry to determine the eastward component. Since it forms a right angle with the northward direction, you can use the sine function. The eastward component can be found using the formula: Eastward Component = Magnitude of Velocity * sine(angle with north).
In this case, the eastward component = 550 kph * sin(45 degrees).
4. Calculate the values using a scientific calculator or software. The cosine of 45 degrees is approximately 0.7071, and the sine of 45 degrees is also approximately 0.7071.
Therefore, the northward component = 550 kph * 0.7071 ≈ 389.1 kph.
And the eastward component = 550 kph * 0.7071 ≈ 389.1 kph.
So, the northward component of the velocity is approximately 389.1 kph, and the eastward component is also approximately 389.1 kph.