Calculus Project: Position eq with Theta

[seansss]

Hey all I am trying to do a calculus project that deals with the flight of an arrow. At first glance I thought I would be using the eq s(t)=-16t^2+VT+S...V being the initial velocity, S initial height, and T for time. I quickly figured out that I needed to have a theta in there some where to account for the launch angle. Any help would be appreciated thanks.


sean

 

[mathman]

Hey all I am trying to do a calculus project that deals with the flight of an arrow. At first glance I thought I would be using the eq s(t)=-16t^2+VT+S...V being the initial velocity, S initial height, and T for time. I quickly figured out that I needed to have a theta in there some where to account for the launch angle. Any help would be appreciated thanks.


sean

Strictly speaking you have 2 equations, since V is a vector quantity.

h(t)=-16t^2+ut+s and p(t)=wt, where u is the vertical component of the initial velocity and w is the horizontal. s is the initial height, while the starting horizontal is 0. h(t) and p(t) are the height and position in time. In reality you should take into account air resistance, but that is a much harder problem.

 

[astrokreng]

,

It's great that you are working on a calculus project that involves the flight of an arrow. It sounds like you have a good understanding of the basic equation for position, s(t)=-16t^2+VT+S, where V is the initial velocity, S is the initial height, and T is time. However, you are correct in realizing that you need to include the launch angle, theta, in your equation as well.

In order to account for the launch angle, you will need to incorporate the horizontal and vertical components of the initial velocity. This can be done by using trigonometric functions, such as sine and cosine, to find the horizontal and vertical components respectively. Then, you can use these components in your position equation to account for the launch angle.

I would also suggest looking into the concept of parametric equations, which are commonly used in projectile motion problems and involve using both x and y coordinates to describe the motion. This may be helpful in incorporating the launch angle into your equation.

I hope this helps and good luck with your project!