Projectile motion-range calculation

In summary, the conversation discusses the trajectory of a stone thrown from the top of an inclined hill at an initial speed and angle. The formula for calculating the distance covered by the stone is provided, but the speaker is having trouble understanding and solving it. They mention using a labelled diagram, resolving the launch velocity into vertical and horizontal components, and establishing the time taken to cover a certain distance. The conversation ends with the speaker seeking guidance on how to continue solving the problem.
  • #1
Apleo
9
0
Warning! Posting template must be used for homework questions. Effort must be shown in the Attempt at a Solution.
1. the surface of a hill is inclined at α to horizontal,a stone is thrown from the top of the hill at initial speed u at angle β with vertical line. How far from the top will the stone strike the ground?

2. R=(u^2 sin2θ)\g or by rotational co ordinate geometry3. can't prove that the dist covered by the stone is 2(u^2 sinβcos(α-β))\gcos^2 α
 
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  • #2
How did you go about trying to solve this? Where is your labelled diagram ?

The provided answer is correct, it's the distance measured along the sloping ground
 
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  • #3
shall i send you a labelled diagram
 
  • #4
How shall i start the calculation?
 
  • #5
Apleo said:
shall i send you a labelled diagram
Attach a jpeg to your forum post.
 
  • #6
the curve of projectile is not perfect...if you cannot understand please ask! AND sorry for late reply!
 

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  • #7
The launch velocity can be shown resolved into 2 components.

The time taken to cover distance CB can be established.
 
  • #8
i had tried but got stuck!
 
  • #9
Apleo said:
i had tried but got stuck!
Show the working of your attempt.
 
  • #10
i had got confused with it because the projectile had exceeded its range so i can't solve it , i just checked mine calculation its wrong so suggest me how to start!
 
  • #11
It has to be worked using algebra, as no numerical data is provided.

Can you resolve the launch velocity into vert and horiz components?

Using your diagram, CB is the horizontal distance the projectile travels, because after traveling for that time & distance it hits terrain.
 
  • #12
yes i had resolved it into vert & hoz components...but after that what should i do?
 
  • #13
"
Apleo said:
yes i had resolved it into vert & hoz components...
Well, what is your answer---how do you express the components of its initial velocity?
 
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What is projectile motion and why is it important to calculate range?

Projectile motion refers to the motion of an object that is launched into the air and moves under the influence of gravity. It is important to calculate range because it helps us understand the trajectory of an object and predict where it will land, which is crucial for many practical applications such as sports, engineering, and military operations.

What are the key factors that affect the range of a projectile?

The key factors that affect the range of a projectile are the initial velocity, the angle of launch, and the gravitational force. Other factors such as air resistance, wind, and elevation may also have an impact, but they are usually considered negligible.

How do you calculate the range of a projectile?

The range of a projectile can be calculated using the formula: R = (v2 * sin 2θ) / g, where R is the range, v is the initial velocity, θ is the angle of launch, and g is the gravitational acceleration (9.8 m/s2 on Earth). This formula assumes a level launch and no air resistance.

What is the maximum range of a projectile?

The maximum range of a projectile occurs when it is launched at an angle of 45 degrees. This is because at 45 degrees, the initial velocity is divided equally between the horizontal and vertical components, resulting in the maximum range. Any angle greater than 45 degrees will result in a shorter range.

How does air resistance affect the range of a projectile?

Air resistance can decrease the range of a projectile by slowing it down as it travels through the air. This is because air resistance creates a drag force that acts in the opposite direction of the projectile's motion. The greater the air resistance, the shorter the range of the projectile will be.

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