Proof of Projectile Motion: Displacement and Gravity Explained

In summary, when a body is thrown horizontally from a cliff, its displacement is equal to its initial horizontal speed multiplied by the time it takes to reach the ground. The reason for considering gravity in this scenario is because it affects the time taken for the object to move in the horizontal direction. This is important to note when calculating the range of the object's motion.
  • #1
Jadaav
175
1
A body is thrown horizontally from a cliff with an initial horizontal speed. It hits the ground at a distance X from its initial position. It is said that the displacement = horizontal speed * time.

When the body falls, gravity acts upon it. So why don't we consider gravity ?

Any proof that the displacement would be the same as above if the same body would have moved with the same initial speed on a flat horizontal path for the same time period ?

Of course in the 2nd situation, it would continue to move infinitely.
 
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  • #2
Jadaav said:
When the body falls, gravity acts upon it. So why don't we consider gravity ?
Of course you must consider gravity. The vertical motion under gravity determines how quickly the body reaches the ground and thus how far it's able to get horizontally before it lands.
 
  • #3
Then range = horizontal speed * time is false ?
 
  • #4
Jadaav said:
Then range = horizontal speed * time is false ?

What determines the "time"? It is the fall of the object due to gravity!

While gravity doesn't affect the motion in the horizontal direction, it affects the time taken for the object to move! That is how gravity comes in!

You should go back and resolve this problem, and pay attention to what factors determine the time of motion that you used for the horizontal component.

Zz.
 
  • #5
Ok thanks for clearing my doubt on the subject. I didn't give much thought on the time which is already affected by gravity.
 

What is projectile motion?

Projectile motion refers to the motion of an object that is moving through the air due to the force of gravity. It is a combination of horizontal and vertical motion, and follows a curved path called a parabola.

What is the equation for projectile motion?

The equation for projectile motion is y = y0 + v0yt + 1/2at2 for the vertical motion, and x = x0 + v0xt for the horizontal motion. Where y and x are the vertical and horizontal positions, y0 and x0 are the initial positions, v0y and v0x are the initial velocities, t is time, and a is acceleration due to gravity.

What is the importance of proof for projectile motion?

The proof for projectile motion is important because it helps us understand and predict the motion of objects in real-world scenarios, such as the trajectory of a ball being thrown or a rocket being launched. It also allows us to calculate important factors such as the maximum height and range of a projectile.

How is air resistance accounted for in projectile motion?

Air resistance is often ignored in basic projectile motion calculations, but it can be accounted for by adjusting the value of acceleration due to gravity. In more complex situations, air resistance can be modeled using equations that take into account the shape and size of the object, as well as the density and viscosity of the air.

What are some real-world applications of projectile motion?

Projectile motion has many real-world applications, such as calculating the trajectory of a golf ball, predicting the path of a thrown baseball, or determining the range of a missile. It is also used in sports, engineering, and physics research. Understanding projectile motion is essential for designing and launching space vehicles and studying the motion of objects in the Earth's atmosphere.

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