What is the Optimal Throw Angle with Horizontal Wind Force?

[PhyNewie]

Homework Statement

What is the thrown angle of a body with a weight w, to make the maximun height equal to the horizontal lenght. Also exists a horizontal wind's force F that acts over the body?

The Attempt at a Solution

I think these are the relations, or i am wrong?
1. (Vo^2.sin^2$$\alpha$$)/2g = (Vo^2.sin$$\alpha$$)/g
2. Vox = Vox . Cos$$\alpha$$ - F
Voy = Voy sen$$\alpha$$ - W

 

[aim1732]

Equated range with max. height but range changes with the horizontal force. The other two relations I do not understand. Could you please tell us what you are thinking?

 

[PhyNewie]

Equated range with max. height but range changes with the horizontal force. The other two relations I do not understand. Could you please tell us what you are thinking?

The other relations are just the initial velocity of the body in the x-axis and in the y axis. I am trying to use that relations to solve the problem, they are not part of the problem

The problem is to calculate the angle, and the conditions are: - the max height = horizontal length , also the wind force F acts over the body, also is considered the weight of the body.

I suposse that the wind force F changes the body velocity in the x-axis so there an desaceleration, and the body's weight w modifies the movement in the y axis, so what could the relations to solve that.

 

[aim1732]

I think you need to stop guessing.
Apply the equations of motion along the horizontal and vertical directions separately. Calculate range and max. height and equate them. Trying to use the standard formulae for projectiles is confusing you.

 

[rwisz]

I would first clarify the terms used in the problem. It seems that the problem is asking for the optimal angle at which to throw a body with weight w, in order to achieve the maximum height equal to the horizontal length. Additionally, there is a horizontal wind force F acting on the body.

To solve this problem, we can use the kinematic equations to determine the optimal angle. The first equation, (Vo^2.sin^2\alpha)/2g = (Vo^2.sin\alpha)/g, relates the initial velocity (Vo) of the body, the angle of the throw (alpha), and the acceleration due to gravity (g) to the maximum height achieved by the body. This equation assumes no external forces acting on the body.

However, in this problem, there is a horizontal wind force F acting on the body. This means that the horizontal velocity of the body (Vox) will be affected by this force. The second equation, Vox = Vox . Cos\alpha - F, takes into account this horizontal force and allows us to calculate the horizontal velocity of the body.

Finally, we can use the third equation, Voy = Voy sen\alpha - W, to calculate the vertical velocity of the body, taking into account the weight of the body (W). By manipulating these equations, we can find the optimal angle at which to throw the body in order to achieve the desired maximum height.

In conclusion, the problem can be solved using the kinematic equations, taking into account the external horizontal force and the weight of the body. With these calculations, we can determine the optimal angle for the throw.