The compass in a plane indicates that the plane is heading due east, with an airspeed of 250 km/h (Vpa). A steady wind is blowing with a magnitude of 75km/h, which increases the velocity of the plane, relative to the ground. If the plane is going along a direction East 12 degrees North, what is the magnitude of the plane’s velocity relative to the ground?

Answer: 299 km/h

I feel like I can't answer this question unless I know the angle in which the wind is blowing. Can someone tell me how to approach this problem please

To solve this problem, you can use vector addition to find the magnitude of the plane's velocity relative to the ground. Here are the steps to approach this problem:

Step 1: Draw a diagram

Start by drawing a diagram to visualize the problem. Draw a vector to represent the plane's velocity relative to the ground (Vpg) pointing in the East 12 degrees North direction. Also, draw a vector to represent the velocity of the wind (Vw), pointing in the direction the wind is blowing.

Step 2: Break down vectors into components

Break down the vectors Vpg and Vw into their respective components along the East and North directions. To do this, you can use basic trigonometry. Vpg has a magnitude of 250 km/h and is directed at an angle of 12 degrees North of East. So, the East component (Vpg,E) of Vpg can be calculated using:

Vpg,E = 250 km/h * cos(12 degrees)

Similarly, the North component (Vpg,N) of Vpg can be calculated using:

Vpg,N = 250 km/h * sin(12 degrees)

Step 3: Account for the effect of wind

Since the wind is blowing with a magnitude of 75 km/h, it adds to the velocity of the plane relative to the ground. The wind vector (Vw) can be broken down into East and North components using the same approach as in step 2.

Step 4: Add the components

Now, add the East components and North components, separately, to find the combined East and North components of the plane's velocity relative to the ground.

Vpg,E_final = Vpg,E + Vw,E
Vpg,N_final = Vpg,N + Vw,N

Step 5: Calculate the magnitude of the resulting vector

To find the magnitude of the resulting vector Vpg_final, use the Pythagorean theorem:

Vpg_final = √(Vpg,E_final^2 + Vpg,N_final^2)

Plug in the values you obtained from step 4 and calculate the magnitude.

Step 6: Round the answer

Finally, round the resulting magnitude to the appropriate number of significant figures. In this case, since all inputs have 2 significant figures, round the result to 3 significant figures.

By following these steps, you should arrive at the answer of 299 km/h for the magnitude of the plane's velocity relative to the ground.