Helicopter Speed Relative to Ground: Solve w/ Vector Components

[Delber]

Homework Statement

A helicopter's velocity relative to the air is 55m/s[W35$$^\circ$$N]
The wind speed is 21 m/s[E].
I need to find the speed of the airplane relative to the ground.

Homework Equations

The Attempt at a Solution

I tried using vector components for this equation. Since the vertical component of the vector of the helicopters speed relative to the air is the same as the vector of the helicopters speed relative to the ground and the horizontal component should be the horizontal component of the helicopter's velocity relative to the air minus the wind speed.
I tried it this way and the answer is different from the one given by the textbook. I'm not very confident with vector components.

Edit: I did it using the cosine law and got the correct answer, but I would like to know if there was any faults with the way I tried to do it with vector components.

 

[jk4]

There doesn't appear to be any faults with your description of using vectors. Perhaps you just made an error.

 

[Moetasim]

I would like to commend you for using vector components to solve this problem. Vector components are a powerful tool for solving problems involving motion in multiple directions. However, it is important to make sure that you are using the correct components and that your calculations are accurate.

In this case, it looks like you may have made a mistake in identifying the vertical component of the helicopter's velocity relative to the air as the same as the helicopter's velocity relative to the ground. While this may be true for some cases, it is not always the case. The vertical component of the helicopter's velocity relative to the air would actually be the sine component, not the cosine component. This means that the vertical component of the helicopter's velocity relative to the ground would be slightly different from the vertical component of the helicopter's velocity relative to the air.

It is also important to double check your calculations to make sure you are using the correct values for the angle and magnitude of the vectors. Small errors in these values can lead to significant differences in the final answer.

In this case, using the cosine law may have been a more accurate approach to solving the problem. However, it is always good to have multiple methods for solving a problem and to check your work to ensure accuracy. Keep practicing and improving your skills with vector components, as they are a valuable tool in many scientific and engineering applications.