A novice pilot sets a plane's controls, thinking the plane will fly at 2.50 * 2 to the 2nd power km/h to the north. if the wind blows at 75km/h toward the southeast, what will the plane's new resultant velocity be? use graphical techniques.
Are you sure you don't mean the plane's speed is 2.50*10^2 km/h?
2.50*2^2 = 10 km/h is slower than a bicycle, and lot slower than the wind.
Whatever it is, add the two vectors.
Draw a vector for the plane's speed, pointing north, with a length of 2.50*10^2 km/h.
Draw a vector for the wind, pointing southeast, with a length of 75 km/h.
The resultant vector is the vector sum of the two vectors.
It will point in the direction of the angle between the two vectors, and have a length equal to the sum of the two lengths.
To determine the plane's new resultant velocity, we need to add the velocity of the plane and the velocity of the wind. The velocity of the plane is given as 2.50 * 2^2 km/h to the north. However, it seems there may be a mistake in the units provided, so I will assume you meant 2.50 * 10^2 km/h to the north instead.
First, we need to break down the velocities into their respective components. Let's assume the positive x-axis points east, and the positive y-axis points north. The velocity of the plane can be expressed as V_plane = (0 km/h, 2.50 * 10^2 km/h) since it is purely in the north direction. The velocity of the wind blowing toward the southeast can be broken down into its x and y components as V_wind = (-75/sqrt(2) km/h, -75/sqrt(2) km/h).
To find the resultant velocity, we need to add the x and y components of the plane's velocity and the wind's velocity separately. The resultant x-component can be calculated as V_x = V_plane_x + V_wind_x = 0 km/h + (-75/sqrt(2) km/h). The resultant y-component can be calculated as V_y = V_plane_y + V_wind_y = 2.50 * 10^2 km/h + (-75/sqrt(2) km/h).
Using your preferred method of calculation, you can now find the values of V_x and V_y. Once you have these values, you can use the Pythagorean theorem to calculate the magnitude of the resultant velocity, which will give you the speed of the plane's new resultant velocity. The angle of the resultant velocity can be determined using inverse trigonometric functions.
I recommend using a graphical technique to better visualize the vectors and find the resultant velocity. Draw a coordinate system, plot the vectors V_plane and V_wind, and then add them head to tail. The resulting vector from the origin to the end of the added vectors will represent the resultant velocity.
I hope this helps you determine the plane's new resultant velocity. Let me know if you have any further questions!
To determine the plane's new resultant velocity, we need to add the velocities of the plane and the wind vectors.
Given:
Plane's speed: 2.50 * 2^2 km/h (let's assume this is equal to 2.50 * 10^2 km/h for a meaningful calculation)
Wind speed: 75 km/h
We can represent the plane's velocity vector as 2.50 * 10^2 km/h in the north direction. Since the wind is blowing towards the southeast, we can represent the wind's velocity vector as 75 km/h in the southeast direction.
To add these vectors graphically, we can draw a coordinate system and represent the plane's velocity vector as a line pointing north with a length of 2.50 * 10^2 km/h. Similarly, we can draw the wind's velocity vector as a line pointing southeast with a length of 75 km/h.
Next, we place the tail of the wind's velocity vector at the head of the plane's velocity vector. To find the resultant vector, we draw a line from the tail of the plane's vector to the head of the wind's vector. The length and direction of this line represent the new resultant velocity.
Using a ruler, we can measure the length of the resultant vector and its direction (angle) relative to the north direction. This will give us the magnitude and direction of the plane's new resultant velocity.