Proving Projectile Farthest Flight at 45° Angle

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In summary, to prove that a projectile flies farthest at a 45 degree angle, you can use the equations of motion to find the time of impact and horizontal distance at that time. Then, find the value of the angle that maximizes the horizontal distance by differentiating the equation and setting it equal to 0. This method is helpful for those who are just starting to learn about differentiation.
  • #1
LENIN
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I know that a projectile flyes the farthest, when it is louncht under a 45 degree angel. But I don't know how to proofe this. Any help would be apreeciated.
 
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  • #2
Well,then can u write down the equations of motion...?

Daniel.
 
  • #3
45 degrees assuming no air resistance!

If the angle is θ degrees, initial speed v, then the horizontal and vertical components of initial velocity are vcos(θ) and vsin(&theta) respectively.

acceleration is 0 horizontally, - g vertically so
velocity (t)= vcos(θ) horizontally, vsin(θ)- gt vertically.

position(t)= vcos(θ)t horizontally, vsin(θ)t- (1/2)gt2 vertically. (taking (0,0) as starting point.)

1. Solve for the time of impact (i.e. set height= 0, find non-zero t solution- it will depend upon θ).

2. Find horizontal distance at that time (again, it will depend upon θ).

3. Find the value of θ that maximizes that (differentiate with respect to θ, set equal to 0).
 
  • #4
Thenks! I got to the 2'nd step myself but the third one is really helpful. I didn't think about useing differentilas, becouse I only started takeing them a few weaks ago and I still don't find my way around very well. Thenks agein.
 

FAQ: Proving Projectile Farthest Flight at 45° Angle

What is the purpose of proving projectile farthest flight at a 45° angle?

The purpose of this experiment is to determine the optimal angle at which a projectile will travel the farthest distance. This can be useful in fields such as physics and engineering, where understanding projectile motion is important.

How is the distance of the projectile flight measured?

The distance of the projectile flight can be measured using a measuring tool, such as a ruler or tape measure. The distance should be measured from the point of launch to the point where the projectile lands.

What variables can affect the distance of the projectile flight?

The distance of the projectile flight can be affected by various factors, including the angle of launch, the initial velocity of the projectile, air resistance, and the mass and shape of the projectile.

How is a 45° angle determined for the experiment?

A 45° angle for the experiment can be determined using a protractor or a digital angle measuring tool. The angle should be measured from the horizontal surface.

What type of projectile can be used for this experiment?

Any type of projectile, such as a ball or a paper airplane, can be used for this experiment as long as it can be launched at a 45° angle and its flight can be accurately measured.

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