Projectile Motion with Air Resistance problem

In summary, the conversation discusses the maximum range of a projectile launched at an angle of theta with air resistance. The participants suggest using the (x-t) and (v-t) equations and finding the derivative of the range equation to determine the angle at which the maximum range occurs. The suggested angle is 53 degrees, but some believe it should be 45 degrees without air resistance. It is mentioned that the formula for air resistance used by the teacher may affect the angle.
  • #1
ahadpoolghaha
1
0
hi.
Suppose that a projectile of mass "m" is launched, from ground level in a horizontal plain, making an angle teta to the horizontal .(with air resistance).now in which angle "m" has the maximum range? .(our teacher said that we should find 53 degrees for teta).please prove it.
(first of all we should find (x-t) and (v-t) equations.then we should find the equation of range with those 2 equations and then we should derivative the rang equation(dr/d(teta).
so we will find the angle in which the mass "m" has the maximum range.this is my idia.if anyone knows the answer of this question,please tell it.i need the diagram of the motion too.)thanks alot.:smile:
 
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  • #2
I think this thread should be in the homework location... none the less you state with air resistance. My understanding is that the equation that describes air resistance is pretty complicated and is normally simplified to either linear or quadratic approximation. But Newtons laws of motion with quadratic drag in horizontal and vertical motion results in a pair of differential equations that can only be solved numerically (there is no general solution).
 
  • #3
Welcome to PF!

ahadpoolghaha said:
… our teacher said that we should find 53 degrees for theta …

Hi ahadpoolghaha! Welcome to PF! :smile:

(I've always understood that it's 45 degrees without air resistance.)

What formula for air resistance did your teacher tell you to use? :smile:
 
  • #4
tiny-tim said:
Hi ahadpoolghaha! Welcome to PF! :smile:

(I've always understood that it's 45 degrees without air resistance.)

What formula for air resistance did your teacher tell you to use? :smile:

I'm pretty sure that theta is always lower than 45 degrees with any plausible
formula for air resistance (linear, quadratic)
 

Related to Projectile Motion with Air Resistance problem

1. What is projectile motion with air resistance?

Projectile motion with air resistance is a type of motion where an object is launched into the air and is affected by both gravity and air resistance. This results in a curved path rather than a straight line.

2. How does air resistance affect projectile motion?

Air resistance is a force that opposes the motion of an object through the air. This force increases as the object's speed increases. In projectile motion, air resistance causes the object to slow down and deviate from its expected trajectory.

3. How is the trajectory of a projectile affected by air resistance?

With air resistance, the trajectory of a projectile will be slightly altered and will follow a curved path rather than a straight line. The amount of curvature will depend on the object's shape, size, and velocity.

4. How do you calculate the effects of air resistance on a projectile?

There are several ways to calculate the effects of air resistance on a projectile, but the most common method is using the drag equation. This equation takes into account the object's velocity, cross-sectional area, and air density to determine the force of air resistance acting on the object.

5. How can air resistance be minimized in projectile motion?

The amount of air resistance can be reduced by making the object more aerodynamic, increasing its initial velocity, or reducing its cross-sectional area. However, it is impossible to completely eliminate air resistance in projectile motion.

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