Projectile Motion Soccer Ball Problem

In summary: So, the acceleration would be 6.042/time, and the time for the object to complete its entire motion is 1.2 seconds- I think you may be able to divide that by 2 to get the time for it to move from its starting position to its maximum height, but I'm not sure because objects do accelerate as they fall so it's motion from the maximum height tp the ground may take a shorter amount of time than its motion from the ground to the maximum height.
  • #1
Balsam
226
8

Homework Statement


I saw this in a video about solving projectile motion problems and I was confused, I think I may have seen the same thing in my textbook:The question says: A soccer player on a level playing field kicks a soccer ball with a velocity of 9.4 m/s at an angle of 40 degrees above the horizontal. Determine the soccer ball's maximum height.

vi=6.042m/s, a=-9.8m/s, vf=o m/s

Homework Equations



vf^2=vi^2+2a(displacement)
3. The attempt at a solutIon
I saw this in a video and I wasn't trying to solve it myself. But, I was confused because the initial velocity used was calculated previously as the initial velocity for the y component of the motion since this is projectile motion and it has 2 components. The final velocity is the velocity at the maximum height- om/s. But, the thing that confused me was that acceleration was stated to be -9.8m/s^2. If this question is taking the initial velocity from when the ball was thrown and the final velocity at the point at which the ball is at its maximum height, is it not then looking at the ball's motion from when it is thrown up until it reaches it's maximum height only- it's looking at the ball's motion as it is moving upwards. So, why is the acceleration given as if the ball were in free fall because that is the acceleration used in problems where an object is in free fall. Sorry this is so long, I just wanted to make sure that what I was saying made sense. Could someone please explain this to me, I'm really confused.
 
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  • #2
You're neglecting air resistance and what not in such projectile motion problems. So the only force acting on the soccer ball is the force of gravity. It is the only source of acceleration. So it is taken as -9.8m/s^2. The - sign is because they took the upward direction to be positive. You could take velocity in the negative direction to be positive and acceleration would be 9.8m/s^2 but your end answer would be the same.
 
  • #3
UncertaintyAjay said:
You're neglecting air resistance and what not in such projectile motion problems. So the only force acting on the soccer ball is the force of gravity. It is the only source of acceleration. So it is taken as -9.8m/s^2. The - sign is because they took the upward direction to be positive. You could take velocity in the negative direction to be positive and acceleration would be 9.8m/s^2 but your end answer would be the same.

How is the ball acceleratng upwards at 9.8m/s^2 when accelleration is equal to vf-vi, which would be -6.042m/s^2? And for this problem, air resistance is not taken into account because this is introductory physics.
 
  • #4
Balsam said:
when accelleration is equal to vf-vi,
Are you sure this is acceleration?
 
  • #5
cnh1995 said:
Are you sure this is acceleration?

Sorry Sheldon, acceleration is equal to change in velocity over time, it should be -6.042/time, and the time for the object to complete its entire motion is 1.2 seconds- I think you may be able to divide that by 2 to get the time for it to move from its starting position to its maximum height, but I'm not sure because objects do accelerate as they fall so it's motion from the maximum height tp the ground may take a shorter amount of time than its motion from the ground to the maximum height. In which case, I think it would be wrong to divide the time by 2 and say that it takes an equal amount of time for the ball to move from the ground to the max height as it takes for the ball to move from the max height to the ground.
 
  • #6
Balsam said:
How is the ball acceleratng upwards at 9.8m/s^2
Who said the ball was accelerating upward? An upward velocity is taken to be positive, and acceleration due to gravity is taken to be -9.8 m/s2, which means that while the initial velocity of the kicked ball is upward, that velocity is decreasing while it is aloft. Eventually, the velocity of the ball upward reduces to zero, after which, the ball falls back to the ground.

when accelleration is equal to vf-vi, which would be -6.042m/s^2? And for this problem, air resistance is not taken into account because this is introductory physics.
You should be careful with units here. Adding to subtracting like units results in like units.
 
  • #7
SteamKing said:
Who said the ball was accelerating upward? An upward velocity is taken to be positive, and acceleration due to gravity is taken to be -9.8 m/s2, which means that while the initial velocity of the kicked ball is upward, that velocity is decreasing while it is aloft. Eventually, the velocity of the ball upward reduces to zero, after which, the ball falls back to the ground.You should be careful with units here. Adding to subtracting like units results in like units.
I'm still confused- I thought an acceleration of -9.8m/s^2 was limited to objects in free fall
 
  • #8
Balsam said:
I'm still confused- I thought an acceleration of -9.8m/s^2 was limited to objects in free fall
When a body is moving with some velocity v and a force is applied on it, component of velocity along the line of action of force changes. This means, along the direction of force, body has acceleration. Here, gravity is in acting in y direction, hence, y component of velocity is affected. Hence, g=9.8m/s2 is applicable here for the y component of the velocity.
 
  • #9
cnh1995 said:
When a body is moving with some velocity v and a force is applied on it, component of velocity along the line of action of force changes. This means, along the direction of force, body has acceleration. Here, gravity is in acting in y direction, hence, y component of velocity is affected. Hence, g=9.8m/s2 is applicable here for the y component of the velocity.

But, it's not falling down- it's moving upwards. I don't understand.
 
  • #10
"Sheldon" is right mate. What you have taken as vf is not actually vf at all. It is only the vertical component of vf. Look at it this way: Is there any force acting in the horizontal direction to bring about a change in the horizontal component of the velocity of the ball? If there isn't why should that horizontal component change?
 
  • #11
Balsam said:
But, it's not falling down- it's moving upwards. I don't understand.
Why does a ball thrown vertically upwards stop at some point? What affects its upward journey?
 
  • #12
A downward acceleration does not necessarily mean that the object itself must move downwards. Look at the vertical component of the velocity of the ball. It is decreasing, so there must be a force acting in the opposite direction to the direction of the vertical component. The ball moves upwards with decreasing velocity so there must be a force and hence an acceleration acting in the opposite direction.
Also the ball does eventually start falling down. After it reaches its maximum, it
 
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  • #13
UncertaintyAjay said:
"Sheldon" is right mate. What you have taken as vf is not actually vf at all. It is only the vertical component of vf. Look at it this way: Is there any force acting in the horizontal direction to bring about a change in the horizontal component of the velocity of the ball? If there isn't why should that horizontal component change?
But we're only looking at this in terms of the y component because we want to find its max height, which has to do with the y component, not the x component
 
  • #14
Balsam said:
But, the thing that confused me was that acceleration was stated to be -9.8m/s^2. If this question is taking the initial velocity from when the ball was thrown and the final velocity at the point at which the ball is at its maximum height, is it not then looking at the ball's motion from when it is thrown up until it reaches it's maximum height only- it's looking at the ball's motion as it is moving upwards. So, why is the acceleration given as if the ball were in free fall because that is the acceleration used in problems where an object is in free fall. Sorry this is so long, I just wanted to make sure that what I was saying made sense. Could someone please explain this to me, I'm really confused.
The ball performs a 2-dimensional motion, it moves both vertically and horizontally. If you set up a coordinate system with horizontal x-axis pointing to the right and vertical y-axis pointing upward, then both components of the initial velocity are positive. The acceleration points vertically downward during the whole motion, so ay=-9.81 m/s2 and ax=0.
 
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  • #15
cnh1995 said:
Why does a ball thrown vertically upwards stop at some point? What affects its upward journey?

Gravity- so even as in object is traveling upwards, it's acceleration is still -9.8m/s^2?
 
  • #16
ehild said:
The ball performs a 2-dimensional motion, it moves both vertically and horizontally. If you set up a coordinate system with horizontal x-axis pointing to the right and vertical y-axis pointing upward, then both components of the initial velocity are positive. The acceleration points vertically downward during the whole motion, so ay=-9.81 m/s2 and ax=0.
So even as an object is moving upwards freely, its acceleration is still -9.8m/s^2?
 
  • #17
Balsam said:
Gravity- so even as in object is traveling upwards, it's acceleration is still -9.8m/s^2?
Right. The ball will be decelerating, hence the minus sign.
 
  • #18
Yes. The reason I mentioned the horizontal component was because I was not entirely sure you understood that the acceleration in this case will be independent of the horizontal components of velocity. Also change in velocity is not acceleration which was the point "Sheldon" was trying to make.
 
  • #19
cnh1995 said:
Right. The ball will be decelerating, hence the minus sign.

Okay, makes sense. Thank you.
 
  • #20
Incidentally watch one of Walter Lewin's lectures on youtube. There is one on projectile motion. It will really clear things up for you.
 
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  • #21
Balsam said:
So even as an object is moving upwards freely, its acceleration is still -9.8m/s^2?
Yes. The Earth is there, and attracts every object towards it center. At the surface of the Earth, this attractive force is mg. If the body is in air, it accelerates downward with the same acceleration, either moving upward or downward. When moving upward, the speed decreases due to this negative acceleration and the speed increases when the body is moving downward.
 
  • #22
UncertaintyAjay said:
Yes. The reason I mentioned the horizontal component was because I was not entirely sure you understood that the acceleration in this case will be independent of the horizontal components of velocity. Also change in velocity is not acceleration which was the point "Sheldon" was trying to make.

Yes, I realized that eventually. Also, perhaps a joke about physics would've been more well received than a stupid big bang joke haha.
 
  • #23
UncertaintyAjay said:
Incidentally watch one of Walter Lewin's lectures on youtube. There is one on projectile motion. It will really clear things up for you.
Yeah. He's the best!
 
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What is projectile motion?

Projectile motion is the motion of an object through the air, under the influence of gravity. It follows a curved path due to the combination of its horizontal and vertical components of motion.

Why is projectile motion important in soccer?

Projectile motion is important in soccer because it helps players understand and predict the trajectory of the ball when kicked or thrown. This knowledge is crucial for accurate passes, shots, and saves.

How do you calculate the initial velocity of a soccer ball in projectile motion?

The initial velocity of a soccer ball can be calculated by measuring the distance and time of flight of the ball, and then using the formula v = d/t. This will give you the initial velocity in meters per second (m/s).

What factors affect the trajectory of a soccer ball in projectile motion?

The trajectory of a soccer ball in projectile motion is affected by the initial velocity, angle of projection, air resistance, and gravity. Other factors such as wind and surface conditions can also have an impact.

How can understanding projectile motion improve a soccer player's performance?

Understanding projectile motion can help a soccer player improve their performance by allowing them to make more accurate passes, shots, and saves. It also helps players anticipate the movement of the ball and make strategic decisions on the field.

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