Max distance when an angle for a projectile is pi/4 neglecting air resistance

In summary, the formula for calculating the maximum distance of a projectile at an angle of pi/4 is D = V^2 / g, where D is the maximum distance, V is the initial velocity, and g is the acceleration due to gravity. Neglecting air resistance will cause an overestimation of the maximum distance, as air resistance reduces the velocity of the projectile. The maximum distance can never be greater than the initial velocity, and increasing the initial velocity will result in a greater maximum distance. The mass of the projectile also affects the maximum distance, but only by a constant value in the formula. Therefore, the initial velocity has a greater impact on the maximum distance compared to the mass.
  • #1
Dustinsfl
2,281
5
We know that the angle of \(\frac{\pi}{4}\) causes a projectile to travel its max distance when air resistance is neglected.

When we consider air resistance is the \(\frac{\pi}{4}\) still the angle that produces the max distance? With air resistance, the projectile with of course travel less than the distance without air resistance though.
 
Mathematics news on Phys.org
  • #2

FAQ: Max distance when an angle for a projectile is pi/4 neglecting air resistance

What is the formula for calculating the maximum distance when an angle for a projectile is pi/4?

The formula for calculating the maximum distance when an angle for a projectile is pi/4 is: D = V2 / g, where D is the maximum distance, V is the initial velocity, and g is the acceleration due to gravity.

How does neglecting air resistance affect the maximum distance of a projectile at an angle of pi/4?

Neglecting air resistance will cause the maximum distance of a projectile at an angle of pi/4 to be overestimated. This is because air resistance acts as a force that opposes the motion of the projectile, reducing its velocity and therefore its maximum distance.

Can the maximum distance of a projectile at an angle of pi/4 ever be greater than the initial velocity?

No, the maximum distance of a projectile at an angle of pi/4 can never be greater than the initial velocity. This is because the initial velocity is a critical factor in determining the maximum distance, and neglecting air resistance only affects the calculation by a constant value (g).

How does increasing the initial velocity affect the maximum distance of a projectile at an angle of pi/4?

Increasing the initial velocity will result in a greater maximum distance for a projectile at an angle of pi/4. This is because the maximum distance is directly proportional to the initial velocity (squared) in the formula D = V2 / g.

Is the maximum distance of a projectile at an angle of pi/4 affected by the mass of the projectile?

Yes, the maximum distance of a projectile at an angle of pi/4 is affected by the mass of the projectile. However, neglecting air resistance, the mass will only affect the maximum distance by a constant value (g) in the formula D = V2 / g. Therefore, the mass will not have a significant impact on the maximum distance compared to the initial velocity.

Similar threads

Back
Top