Calculating the Angle of a Projectile Fired for 3x Range Horizontally

In summary, The conversation discusses a projectile being fired with a horizontal range that is three times its maximum height and determining the angle. Equations of motion are mentioned and one participant is unsure how the 1:3 ratio factors into the problem. The other participant suggests setting up Newton's second law of motion for the system in both directions.
  • #1
jesuslovesu
198
0
A projectile is fired so that its horizontal range is 3 times its max height. What is the angle?

Well, I'm stumped because I thought if I just drew up a triangle and did
arctan(1/3), I would get the correct angle... apparently not.
 
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  • #2
What are the equations of motion?
 
  • #3
hmm

x = vx*t
y = -1/2g*t^2

I'm not really sure where to go, how the 1:3 would factor into anything.
 
  • #4
jesuslovesu said:
hmm

x = vx*t
y = -1/2g*t^2

I'm not really sure where to go, how the 1:3 would factor into anything.
Your equation for y is incorrect.

Set up Newton's second law of motion for the system, both directions!
 

1. How do you calculate the angle of a projectile fired for 3x range horizontally?

To calculate the angle of a projectile fired for 3x range horizontally, you can use the formula:
θ = arctan((4x)/(3v2)), where θ is the angle, x is the range, and v is the initial velocity.

2. What is the significance of calculating the angle of a projectile fired for 3x range horizontally?

Calculating the angle of a projectile fired for 3x range horizontally can help determine the optimal angle for maximum range and distance traveled. It is important in fields such as ballistics and engineering.

3. Can the angle of a projectile fired for 3x range horizontally be calculated using other methods?

Yes, there are other methods for calculating the angle of a projectile fired for 3x range horizontally. Some methods involve using the maximum height of the projectile or the time of flight. However, the formula mentioned above is the most commonly used method.

4. What factors can affect the accuracy of the calculated angle of a projectile fired for 3x range horizontally?

The accuracy of the calculated angle can be affected by factors such as air resistance, wind, and the initial velocity of the projectile. These factors can cause the actual range to differ from the calculated range.

5. How can the calculated angle of a projectile fired for 3x range horizontally be applied in real-life situations?

The calculated angle can be applied in a variety of real-life situations, such as determining the trajectory of a bullet or a missile, designing roller coasters, and calculating the optimal angle for a golf swing or a long jump. It is also used in military operations and space exploration.

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