Concept: Air Resistance in Projectile Motion

[ibwm]

Hi, I am in need for some physics help regarding the effect of air resistance on projectile motion.

My question is "For a tennis ball stuck at an angle of 45 degrees to the horizontal at typical speed without spin, why does air resistance have a greater effect on the horizontal range of the ball rather than the maximum height of the ball?"

I've tried searching Google for a solution, but have yet been able to find one. I don't just want to copy the answer off of the internet, but actually learn the concept.

Any help is much appreciated,
Sharna.

Edit:
In my notes I have:

For launch angle of 45 degrees, Vh and Vv = sin45 and cos45 = 0.707N (I have no idea why it says Newtons here if it's talking about velocity)

And then my notes say: "Theory: Vh= constant = x. Vv= x --> 0 --> x. Average Vh = x (more friction), Average Vv=x/2 (less friction)"

I am still unsure as to what all of this means. What is the reasoning behind the horizontal range being affected more by air resistance than the vertical height? Does it have something to do with friction forces being larger when velocity is larger?

 

[DaveC426913]

Here is a hint: in which case do you feel more wind? Driving at 10mph? Or driving at 60mph?

 

[ibwm]

Here is a hint: in which case do you feel more wind? Driving at 10mph? Or driving at 60mph?

You'd feel more wind driving at 60mph, yeah? I know that there's more friction the faster you are travelling, but I am unsure as to how this affects horizontal distance more than vertical distance. What is the concept behind this?

 

[DaveC426913]

You'd feel more wind driving at 60mph, yeah? I know that there's more friction the faster you are travelling, but I am unsure as to how this affects horizontal distance more than vertical distance. What is the concept behind this?

What is the average velocity of the ball in the y direction as compared the average velocity of the ball in the x direction? They definitely be can't the same since at one point in its trajectory, y velocity is zero.

 

[asteriatic]

Hello Sharna,

Thank you for reaching out for help with understanding the concept of air resistance in projectile motion. I am happy to provide some clarification and explanation.

Firstly, let's define what air resistance is. Air resistance, also known as air drag or aerodynamic drag, is the force that opposes the motion of an object through the air. This force is caused by the air particles colliding with the object as it moves through the air.

Now, to address your question about why air resistance has a greater effect on the horizontal range of a tennis ball rather than its maximum height when launched at a 45 degree angle. The reason for this is due to the nature of air resistance. As an object moves through the air, the air resistance force acts in the opposite direction of the object's motion. This means that when a tennis ball is launched at an angle, the air resistance force will act against the horizontal motion of the ball, reducing its forward velocity. This reduction in velocity leads to a shorter horizontal range.

On the other hand, the air resistance force does not significantly affect the vertical motion of the ball as it is moving in the same direction as the ball's motion. Therefore, the effect of air resistance on the vertical height of the ball is minimal.

To understand this concept further, let's look at your notes. The values of Vh and Vv that you have noted represent the horizontal and vertical components of the ball's initial velocity, respectively. Since the ball is launched at a 45 degree angle, both of these components have the same magnitude, which is equal to the initial velocity of the ball.

Now, when we consider the average velocities, we can see that the average horizontal velocity remains constant (x), while the average vertical velocity decreases to half of its initial value (x/2). This decrease in the vertical velocity is due to the air resistance force acting against it, as explained earlier.

In summary, the reason why air resistance has a greater effect on the horizontal range of a projectile launched at an angle is because the air resistance force acts against the horizontal motion, reducing its velocity and therefore its range. I hope this helps to clarify the concept for you. Keep up the good work in trying to understand the concept rather than just copying the answer from the internet. This will help you to truly learn and understand the concepts of physics.

Best of luck with your studies!
Sincerely,