Projectile motion particle question

In summary, the conversation discusses the projection of a particle with initial velocity v from the origin at an angle of elevation \theta and its movement under gravity. Using equations of motion, the values of v_x and v_y are determined and the maximal height is found by setting v_y to zero. This can be used to find the time at which the particle reaches this height and calculate the range on the horizontal plane.
  • #1
misogynisticfeminist
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A particle is projected from the origin 0 with initial velocity v at an angle of elevation [tex] \theta [/tex] and it moves freely under gravity. Find [tex] tan \theta [/tex] if the greatest height reached by the particle is equals to its range on the horizontal plane.

Using the equations of motion, i have found

[tex] \frac {v^2_y}{ 2g} = v_x t =v_y - 1/2 gt^2 [/tex]

but i am unsure of how to manipulate it from here to find [tex] v_y / v_x [/tex].
 
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  • #2
Use these

[tex]v_x = vcos( \theta)[/tex]
[tex]v_y = vsin( \theta) -gt[/tex]

[tex]x = vcos (\theta)t[/tex]
[tex]y = vsin( \theta)t - g \frac{t^2}{2} [/tex]

Then, the maximal heigth can be determined by realizing that v_y must be zero there. Calculate the time at which this occurs and put it into the formula for y. same goes for x (set y = 0 and calculate the time and put it into x) and then set these two equal to each other

marlon
 
Last edited:
  • #3
hey thanks for the help marlon, I've gotten it...
 

Related to Projectile motion particle question

1. What is projectile motion particle question?

Projectile motion particle question is a problem in physics that involves the motion of an object in a two-dimensional plane under the influence of gravity. It is commonly used to study the motion of objects such as projectiles, which are launched into the air and then move along a curved path due to the force of gravity.

2. What are the factors that affect projectile motion?

The factors that affect projectile motion include the initial velocity of the object, the angle at which it is launched, the force of gravity, and any external forces acting on the object such as air resistance or wind.

3. How is the trajectory of a projectile determined?

The trajectory of a projectile is determined by its initial velocity, launch angle, and the force of gravity. These factors can be analyzed using mathematical equations such as the projectile motion equation, which calculates the position, velocity, and acceleration of the object at any given time.

4. Can the motion of a projectile be predicted accurately?

In theory, the motion of a projectile can be predicted accurately using mathematical equations. However, in real-world situations, factors such as air resistance, wind, and variations in initial conditions can affect the accuracy of the predictions.

5. How is projectile motion useful in real-life applications?

Projectile motion is used in various real-life applications, such as sports, engineering, and military operations. It is used to calculate the trajectory of objects like balls, bullets, and rockets, and to design structures such as bridges and buildings that can withstand the force of gravity and other external forces.

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