# Projectile Motion Proof/Hassle

• Varaia
In summary, the conversation is about solving various relations involving angles and trigonometric functions. The first relation is Rsin2theta+d(1+cos2theta)=(R^2)/Rnot, where Rnot= ((vnot)^2)/g. The next relation is Rm(meaning maximum R) happens for tan2(thetamax)=Rm/d. The third relation is 2thetamax+alpha=90 degrees. Finally, the fourth relation is (Rnot^2)+2dRnot=Rm^2. The person is struggling to solve the first relation and is looking for help with trigonometric identities.
Varaia
This is a real pain and I'm getting nowhere. If you can't see the image look at the attached file.

Angle a(upper angle)=Theta Angle b(lower angle)=Beta
Prove these relations:
a) Rsin2theta+d(1+cos2theta)=(R^2)/Rnot where Rnot= ((vnot)^2)/g
b) That Rm(meaning maximum R) happens for tan2(thetamax)=Rm/d
c) 2thetamax+alpha=90 degrees
d) (Rnot^2)+2dRnot=Rm^2

For a) I'm getting down to 2costheta(Rsintheta+dcostheta)=(R^2)/Rnot
But I don't see the next step, maybe I went too far. Or do I need to include Beta somewhere? I don't think I do. There is some trig relation or relating it to the diagram that I just don't see.
All I really need is help on a)then
I can use what I know from a) to solve for b) and each one after can be done likewise however I won't get to them if I can't get a) done.

#### Attachments

• projectile.JPG
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## 1. What is projectile motion?

Projectile motion is the motion of an object through the air or space under the influence of gravity. It follows a curved path known as a parabola.

## 2. How is projectile motion proved?

Projectile motion can be proved using mathematical equations and principles such as Newton's laws of motion and the equations of motion. Additionally, experimental data can also be used to prove projectile motion.

## 3. What are the factors that affect projectile motion?

The factors that affect projectile motion include the initial velocity, angle of projection, air resistance, and gravitational force. The mass and shape of the object can also have an impact on its trajectory.

## 4. Can projectile motion be a hassle?

Projectile motion can be a hassle when considering factors such as air resistance, which can complicate the calculations and make it more difficult to predict the motion accurately. Additionally, in real-world situations, there may be other external factors that can affect the motion of the object, making it more challenging to prove.

## 5. How is projectile motion used in real life?

Projectile motion is used in various real-life applications, such as sports, military technology, and space exploration. For example, in sports, understanding projectile motion can help athletes improve their performance in throwing, kicking, or hitting objects. In military technology, projectile motion is used to design weapons and ammunition. In space exploration, it is used to calculate the trajectories of spacecraft and objects in orbit.

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