# Solving Projectile Motion Equation for Distance

• roldy
In summary, the conversation discusses the creation of a distance equation for a projectile launched at an angle from a certain height. The knowns and unknowns of the problem are listed, with the knowns including the mass of the projectile and the distance to the ground from the pivot point of the pole. The unknowns include the velocity of the projectile, final distance, and angles alpha and beta. The conversation also mentions the use of conservation of energy and integrating over the given angles to solve the problem. The final equation is still being worked on.
roldy
Could someone help me come up with the distance equation for a projectile that is launched at an angle and initially at a height. I need figure out a relationship between distance, alpha, and beta. The final equation should contain only variables d, alpha, and beta.

The knowns:
1. The mass of the projectile is .021 kg
2. The distance from the pivot point of the pole to the ground is .2 meters

The unknowns:

1. The velocity of the projectile when the pole is at angle beta
2. The final distance
3. The angles beta and alpha

Here's what I've tried to do:

I started with the conservation of energy.
KE1=0
PE1=mgh1
KE2=1/2mV22
PE2=mgh2

I think I have solved this problem. I will scan in my work sometime and would like to see if I'm on the right track. If anyone could help with this problem it would be awesome. This problem is a theoretical problem for a design project I'm working on.

#### Attachments

• diagram.jpg
27.4 KB · Views: 413
I think you need to be specific as to how the system actually works. Is the long pole rotating clockwise while applying a force on the projectile from angle alpha to beta? If this is the situation, then you can get an equation involving F, alpha, beta, and d. You would not be able to get an equation with just alpha, beta, and d (d is completely dependent on the force applied over the range theta=alpha to theta=beta).

If you had the force as a function of theta, then you could integrate over theta=alpha to theta=beta to get the work done, and then from there you can deduce the kinetic energy, velocity direction, and position upon release, and it becomes elementary.

Sorry about that, the long pole does rotate clockwise. The force that is applied to this system is done by a spring that will be attached from the pole to the front of the setup. I know that as the pole will be rotated back initially the spring will get stretched around the shaft a little but I'm neglecting that. In the equations I have derived, I will optimize the angles alpha, beta and the energy of the spring using the excel solver tool. Attached is what I think the equation looks like.

#### Attachments

• equations.doc
133.5 KB · Views: 157
So I see everyone gave up.

## 1. What is projectile motion?

Projectile motion is the motion of an object that is launched into the air and then follows a curved path due to the influence of gravity. Examples of projectiles include a thrown baseball, a kicked soccer ball, or a launched rocket.

## 2. How do you calculate the distance of a projectile?

The distance of a projectile can be calculated using the equation: d = v0 * t + (1/2) * a * t2, where d is the distance, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (9.8 m/s2).

## 3. What information is needed to solve the projectile motion equation for distance?

To solve the projectile motion equation for distance, you will need to know the initial velocity of the object, the time it takes to reach the desired distance, and the acceleration due to gravity.

## 4. Is the angle of launch important in projectile motion?

Yes, the angle of launch is important in projectile motion because it affects the shape of the trajectory and the distance traveled. The optimal angle for maximum distance is 45 degrees.

## 5. What are some real-life applications of projectile motion?

Projectile motion has many real-life applications, including sports such as baseball, soccer, and basketball, as well as in fields like physics, engineering, and military technology. Understanding projectile motion is also essential for activities such as throwing a frisbee or launching a water balloon.

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