Projectile Motion, Finding the Angle

In summary, the problem involves finding the angle of projection for a projectile with a horizontal range equal to three times its maximum height. Using kinematics equations, the problem can be broken down into horizontal and vertical components, and the constraints of constant gravitational force can be factored in to solve for the angle of projection.
  • #1
needlottahelp
29
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Homework Statement


A projectile is fired in such a way that its horizontal range is equal to three times its maximum height. What is the angle of projection?


Homework Equations


Kinematics Equations


The Attempt at a Solution


I'm not even sure where to start. Can someone point me in the right direction?
 
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  • #2
Lotta, as soon as you see the word "projectile", separate the initial velocity v at angle A into horizontal and vertical parts. Then write two headings:
Horizontal and Vertical. Decide in each case whether you have constant speed or accelerated motion and write the appropriate formula(s). Put in the numbers or expressions for all known quantities and look for an equation you can solve.
 
  • #3
ok so I tried fitting the x and y components into various kinematics equations but I can't seem to isolate any variables to find the angle
I get things like
19.6h = Vy^2
or 3h = Vx t
any hints?
 
  • #4
needlottahelp said:
ok so I tried fitting the x and y components into various kinematics equations but I can't seem to isolate any variables to find the angle
I get things like
19.6h = Vy^2
or 3h = Vx t
any hints?

Write out the traditional equations of motion for us for a constant gravitational force. What are the general equations? Now, what constrains this problem? How can you factor those constraints into those equations? Write things out and show us your work.
 

1. What is projectile motion?

Projectile motion is the motion of an object through the air or space under the influence of gravity, with only the force of gravity acting on it.

2. How is the angle of a projectile's trajectory determined?

The angle of a projectile's trajectory is determined by the initial velocity at which it is launched and the force of gravity acting on it. This is known as the launch angle or the angle of projection.

3. Why is it important to calculate the angle of a projectile's trajectory?

Calculating the angle of a projectile's trajectory is important because it allows us to predict the path of the projectile and determine where it will land. This is useful in a variety of fields, such as sports, engineering, and physics.

4. How is the angle of a projectile's trajectory related to its range?

The angle of a projectile's trajectory is directly related to its range, or the distance it travels. The optimal angle for maximum range is 45 degrees, as this angle allows for the greatest horizontal displacement before the projectile hits the ground.

5. What factors can affect the angle of a projectile's trajectory?

The angle of a projectile's trajectory can be affected by factors such as air resistance, wind speed and direction, and the shape and weight of the object. These factors can change the trajectory of the projectile and therefore impact the angle at which it is launched.

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