# Calculus Project: Position eq with Theta

• seansss
In summary, the conversation is about a calculus project dealing with the flight of an arrow. The equation s(t)=-16t^2+VT+S is mentioned, with V representing initial velocity, S representing initial height, and T representing time. It is noted that a theta is needed to account for the launch angle. There are actually two equations involved, one for vertical height and one for horizontal position. Taking air resistance into account would make the problem more difficult.

#### 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

seansss said:
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.

## 1. What is the purpose of a position equation with theta in a calculus project?

The position equation with theta is used to describe the position of an object at a given time when it is moving in a circular path. It takes into account the angle (theta) at which the object is located and its distance from the center of the circle.

## 2. How is the position equation with theta derived?

The position equation with theta is derived using trigonometric functions and parametric equations. It involves finding the x and y coordinates of the object in terms of the angle (theta) and the radius of the circle.

## 3. What is the difference between a position equation with theta and a regular position equation?

A regular position equation describes the position of an object in terms of time, while a position equation with theta describes the position of an object in terms of the angle (theta) at which it is located in a circular path. A regular position equation can be used for linear motion, while a position equation with theta is used for circular motion.

## 4. How is a position equation with theta useful in real-life applications?

A position equation with theta is useful in real-life applications such as satellite tracking, planetary motion, and motion of objects on a circular track. It allows us to calculate the position of an object at any given time and predict its future position.

## 5. Are there any limitations to using a position equation with theta?

Yes, there are some limitations to using a position equation with theta. It can only be used for objects that are moving in a circular path, and it assumes a constant angular velocity. It also does not take into account external factors such as air resistance or friction.