Projectiles r = (22sin(x) x 11cos(x))/9.8

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In summary, the conversation is about the best angle to fire a projectile for maximum range. The formula used is r = (22sin(x) x 11cos(x))/9.8, where x is the angle, and it is determined that 45 degrees achieves the most range. However, air resistance affects the range for all angles and for greater air resistance, the angle should be lower than 45 for minimal time in the air. Therefore, considering air resistance, 61 degrees is not the better angle for achieving maximum range.
  • #1
Cummings
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Well, its a debate about what's the best angle to fire a projectile to achieve maximum range.

using the formulae i found

r = (22sin(x) x 11cos(x))/9.8
where x is the angle, 45 gets the most range. But some people say 61 degrees is

using that formulae and ignoring air resistance 61 achives less range than 45.

Air resistance changes the range, yes, but it changes it for all angles.

Is 61 somehow the better angle for air resistance?
 
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  • #2
Assuming no air resistance, the angle for greatest distance is 45 degrees.

Assuming air resistance, the greater the air resistance, the lower you should bring the angle so that the time in the air is minimal.

For air resistance, the angle should be lower than 45 not higher.
 
  • #3


It is difficult to definitively say whether 61 degrees is a better angle than 45 degrees for air resistance without more information. The formula provided takes into account the effects of air resistance, but it is possible that other factors such as wind speed and direction could also play a role in determining the optimal angle for maximum range. Additionally, the type of projectile being fired and its aerodynamic properties could also impact the ideal angle. Therefore, it is important to consider all variables and conduct further analysis before determining the best angle for a projectile in a given scenario.
 

1. What is the purpose of the equation "Projectiles r = (22sin(x) x 11cos(x))/9.8"?

The equation is used to calculate the range of a projectile launched at an angle x with an initial velocity of 22 m/s and an initial height of 11 m, taking into account the gravitational acceleration of 9.8 m/s^2.

2. What type of motion does this equation model?

The equation models the motion of a projectile launched at an angle with an initial velocity and height, taking into account the effects of gravity.

3. How does changing the angle x affect the range of the projectile?

Changing the angle x will affect the range of the projectile as it determines the direction and trajectory of the projectile's motion. The range will be maximum when the angle x is 45 degrees.

4. Can this equation be used for any projectile motion?

No, this equation is specifically for projectiles launched at an angle with an initial velocity and height. It does not take into account other factors such as air resistance or non-uniform gravitational fields.

5. What are the units of measurement for the range calculated by this equation?

The range calculated by this equation will have units of meters (m) as it is a measure of distance.

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