Trajectory, Wind Resistance, and Acceleration

In summary, the magnitude of the acceleration of an object thrown upward is highest right after the object is released. This is due to the combination of air resistance and gravity working against the object's initial velocity, resulting in a greater downward acceleration.
  • #1
Soaring Crane
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Suppose the force of wind resistance is proportional to the speed of the object and in the direction opposite of the object’s velocity. If you throw an object upward, when is the magnitude of the acceleration the highest?

a.It is highest at the top of its trajectory.
b.It is the highest right after the object is released.
c.The acceleration of the object is the same throughout the entire trajectory.

I would think that it would be c. but I am unsure of the thought procee for this one. Can anyone give me advice or guide me through this one?

Thanks.
 
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  • #2
Think of the velocities the object has at each of the positions mentioned.
 
  • #3
Now let's look at this qualitatively:
1. When the object is moving UPWARD, then the vertical part of the air resistance add to that of the weight to create a downwards acceleration greater than gravity alone.
What is the case when the object is moving DOWNWARDS?

So, when would the object have the strongest vertical acceleration?

2. In the horizontal component, air resistance steadily retards the object.
So when would the object have the strongest horizontal acceleration?

3. What is then your conclusion?
 
  • #4
This is my attempt at applying what I just read from my posts. Hopefully, I absorbed something after rereading each line.

I was thinking of the velocity vector, but I still only half-understand air resistance. Wouldn't the horizontal component of velocity remain the same? In the vertical direction, wouldn't the initial velocity vector be greatest before the object reaches the top, so the acceleration would be greater when the object just starts to move or after it is released?

Thanks again.
 
  • #5
"Wouldn't the horizontal component of velocity remain the same?"

Nope!
Air resistance force is a vector quantity strictly anti-parallell to the object's velocity vector. Thus, if you start out with some horizontal velocity component, you will also experience a horizontal air resistance component in the opposite horizontal direction.
 
  • #6
I believe it is at its highest right after u throw right? Because air resistance + gravitiy?
 

1. What is trajectory and how does it affect the motion of an object?

Trajectory refers to the path that an object takes as it moves through space. It is affected by various factors such as the initial velocity, gravitational force, and air resistance. The shape and angle of the trajectory can also impact the object's motion, determining how far it will travel and where it will land.

2. How does wind resistance affect the trajectory of an object?

Wind resistance, also known as air resistance, is the force exerted by air molecules on a moving object. It acts in the opposite direction to the object's motion and can significantly impact the trajectory of the object. The greater the wind resistance, the more it will slow down the object and alter its trajectory.

3. What is acceleration and how does it relate to trajectory?

Acceleration is the rate of change of an object's velocity over time. It can be affected by forces such as gravity, air resistance, and friction. In terms of trajectory, the acceleration of an object can determine the shape and angle of its path, as well as how far it will travel before coming to a stop.

4. How do different factors, such as mass and force, affect the trajectory of an object?

The mass of an object and the amount of force acting on it can both impact its trajectory. A heavier object will require more force to accelerate and will therefore have a different trajectory compared to a lighter object. Additionally, the direction and magnitude of the force can also affect the trajectory of an object.

5. How can we calculate the trajectory of an object in real-life situations?

To calculate the trajectory of an object in real-life situations, we can use mathematical equations and principles such as Newton's laws of motion and the equations of motion. We can also take into account external factors like wind resistance and air density to make more accurate predictions of the object's trajectory. Advanced technologies like computer simulations and motion tracking systems can also aid in calculating the trajectory of objects in real-time.

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