Why Is My Projectile Motion Calculation Using Two Angles Incorrect?

In summary, the conversation discusses the difficulty of choosing whether to categorize a physics problem as advanced or introductory. The problem at hand involves finding a solution that is close to the desired result, but the individual is struggling to identify where they are going wrong. Eventually, they realize that they made a simple mistake and the solution is corrected.
  • #1
ChrisEffinSmi
16
0
First, I struggled with whether to put this in advanced or intro physics. I read the sticky, and since this is a 300 level class that is taken at the junior level in the physics BS program at my school, I put it here. If it's considered too simplistic for advanced physics, I apologize.

I've attempted a solution and come up with something painfully close to the desired result, and I have no idea where I'm going wrong. I would really appreciate some insight.


Homework Statement


http://usera.imagecave.com/hotrod73dart/homework/4.8.jpg


The Attempt at a Solution


http://usera.imagecave.com/hotrod73dart/homework/4.8attempted.jpg
 
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  • #2
Your answer fits if you define "elevation" as being measured from horizontal and not from the slope as you have done it.
 
  • #3
Oh gods! How stupid of me! My angle should be [itex]\alpha[/itex] - [itex]\phi[/itex], not just [itex]\alpha[/itex]. That makes my derived answer sin([itex]\alpha[/itex]-[itex]\phi[/itex])*cos([itex]\alpha[/itex]-[itex]\phi[/itex]+[itex]\phi[/itex]) = cos([itex]\alpha[/itex])*sin([itex]\alpha[/itex]-[itex]\phi[/itex]) which is, of course, the desired result. I should sleep more. Thanks for the reply!
 

FAQ: Why Is My Projectile Motion Calculation Using Two Angles Incorrect?

How do you calculate the range of a projectile with two angles?

To calculate the range of a projectile with two angles, you will need to use the range formula: R = (V^2 * sin2θ)/g, where V is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity. However, since there are two angles involved, you will need to calculate the range for each angle and then add them together to get the total range.

What is the optimal angle for maximum range in projectile motion with two angles?

The optimal angle for maximum range in projectile motion with two angles is when the two angles are equal. This means that the projectile is launched at a 45-degree angle from the ground. This angle will give the projectile the maximum range possible, as it allows for equal horizontal and vertical components of the initial velocity.

How does the initial velocity affect the trajectory of a projectile with two angles?

The initial velocity has a direct impact on the trajectory of a projectile with two angles. A higher initial velocity will result in a longer range and a flatter trajectory, while a lower initial velocity will result in a shorter range and a steeper trajectory. However, the angle of launch also plays a role in the trajectory, as a higher angle will result in a higher arc and a lower angle will result in a lower arc.

Can the angle of launch be negative in projectile motion with two angles?

Yes, the angle of launch can be negative in projectile motion with two angles. This occurs when the projectile is launched in the opposite direction of the positive x-axis. The negative angle can be converted to a positive angle by adding 180 degrees to it. However, the final range calculation will still need to be adjusted accordingly.

How does air resistance affect projectile motion with two angles?

Air resistance can have a significant impact on the trajectory of a projectile with two angles. As the projectile moves through the air, it experiences air resistance, which acts in the opposite direction of its motion. This can cause the projectile to deviate from its expected trajectory and result in a shorter range. To account for air resistance, a more complex formula would need to be used in the calculation of the projectile's range.

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