# Helicopter Speed Relative to Ground: Solve w/ Vector Components

• Delber
In summary, the problem involves finding the speed of a helicopter relative to the ground given its velocity relative to the air and the wind speed. The solution can be approached using vector components or the cosine law. The OP attempted both methods but had trouble with the vector component approach, ultimately finding success with the cosine law.
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.

## 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.

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

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.

## What is the formula for calculating helicopter speed relative to ground using vector components?

The formula for calculating helicopter speed relative to ground is v = sqrt(vx^2 + vy^2), where vx and vy are the horizontal and vertical components of the helicopter's velocity, respectively.

## How do you determine the direction of the helicopter’s speed relative to ground?

The direction of the helicopter's speed relative to ground can be calculated using the inverse tangent function, tan^-1(vy/vx). This will give the angle of the helicopter's velocity vector with respect to the horizontal axis.

## Can the helicopter’s speed relative to ground be negative?

Yes, the helicopter's speed relative to ground can be negative if the helicopter is moving in the opposite direction of the chosen reference frame. This means that the vector components vx and vy will have opposite signs.

## How does wind affect the helicopter’s speed relative to ground?

Wind can affect the helicopter's speed relative to ground by either adding to or subtracting from the helicopter's velocity vector components. This means that the helicopter's speed relative to ground will either increase or decrease depending on the direction and magnitude of the wind's velocity vector.

## Can the helicopter’s speed relative to ground be greater than its airspeed?

Yes, the helicopter's speed relative to ground can be greater than its airspeed if the wind is blowing in the same direction as the helicopter's flight path. In this case, the wind's velocity vector will add to the helicopter's airspeed, resulting in a higher speed relative to ground.

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