# Projectile motion parabola shape

• stupif
In summary: The graph is a parabola because the vertical position varies quadratically with the horizontal position. This is due to the constant horizontal velocity and the decreasing vertical velocity caused by gravity. So the shape of the graph is not directly related to the sine function. In summary, the graph of projectile motion's distance against inclination angle is parabolic in shape due to the constant horizontal velocity and decreasing vertical velocity caused by gravity, resulting in a quadratic relationship between vertical and horizontal position. The shape is not directly related to the sine function.
stupif
why the projectile motion's graph distance against inclination angle is parabola shape?
...thank you

do u mean the shape of the distance x as a function of the angle ??

If you are talking about 2d projectile motion with distance v. time for any fixed angle above the horizontal then the graph will be a parabola because distance is quadratic in time i.e. d = v(initial)*t + 1/2*a*t^2.

ya～nerokid

Because the horizontal velocity of the projectile is constant and the vertical velocity continuously decreases because of gravity and hence the distance the projectile traveled in a given time keeps on decreasing and horizontal distance remains the same. This results in a parabolic trajectory.
Thank you.

Newton, my equation is s=([/2] (sin 2 angle))/ g

stupif said:
Newton, my equation is s=([/2] (sin 2 angle))/ g

That's the equation for the maximum horizontal distance the projectile will travel (its range).

But in order to determine the shape of the trajectory, you need to plot vertical postion vs. horizontal position (y vs. x).

x varies linearly with time.

If you eliminate time as a variable, you'll find that y varies quadratically with x.

the lecturer only asks me why the graph of projectile motion is parabolic shape? then what answer should i give??

is it because of the graph is sin graph??s directly proportional to sin angle??

stupif said:
the lecturer only asks me why the graph of projectile motion is parabolic shape? then what answer should i give??

I just explained why in my previous post.

## What is projectile motion?

Projectile motion is the motion of an object through the air under the influence of gravity. It can be described as a parabolic path, meaning the object follows a curved trajectory.

## What factors affect the shape of a projectile's trajectory?

The shape of a projectile's trajectory is affected by its initial velocity, angle of launch, and the force of gravity. These factors determine the shape and height of the parabola.

## Why does a projectile follow a parabolic path?

A projectile follows a parabolic path because it has both a horizontal and vertical component of motion. The horizontal component remains constant, while the vertical component is affected by the force of gravity, resulting in a curved path.

## Can a projectile's path ever be a perfect parabola?

In theory, a projectile's path can be a perfect parabola if there is no air resistance and the gravitational field is uniform. However, in reality, factors such as air resistance and variations in gravitational force can cause slight deviations from a perfect parabola.

## How is the shape of a projectile's path used in real-world applications?

The shape of a projectile's path is used in various real-world applications, such as sports, military weapons, and space exploration. Understanding the trajectory of a projectile can help determine its range, accuracy, and other important factors.

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