TBR Physics Book I Translational Motion Passage question

[missdoctor]

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I don't understand the answer to this question.. It's from the first set of passages Physics Book I, #16. (2009 edition)

You basically have to compare the range (not height) of a ball in two scenarios..

Scenario 1: A ball is initially thrown up at some vertical velocity, and a boy is standing on a cliff exactly where the max height of the ball will reach (implying no vertical velocity). At this max height, the boy pushes the ball with a horizontal velocity of 10m/s.

Scenario 2: The ball this time is initially thrown with a higher vertical velocity, and is pushed at the same exact height as in the first scenario, with the same horizontal velocity of 10m/s (this time though, the ball is not at it's max height so it still has an upward vertical velocity)

So they're asking how will the range vary in the two scenarios. If both the horizontal velocities are the same in both, then won't the range be the same? I thought that vertical and horizontal components are always independent from each other.

Their answer is that the Scenario 2 ball will have a larger range because it has a higher vertical velocity..... but I thought vertical velocity only influenced height and not the horizontal range?

Sorry that was long, thank you so much for any help!

 

[Pons Asinorum]

How much time is the ball in scenario 1 airborne for? What about the ball in scenario 2? Which ball is in the air longer? Which ball is in the air longer after the push by the dude on the cliff? dx = vx * t

I don't understand the answer to this question.. It's from the first set of passages Physics Book I, #16. (2009 edition)

You basically have to compare the range (not height) of a ball in two scenarios..

Scenario 1: A ball is initially thrown up at some vertical velocity, and a boy is standing on a cliff exactly where the max height of the ball will reach (implying no vertical velocity). At this max height, the boy pushes the ball with a horizontal velocity of 10m/s.

Scenario 2: The ball this time is initially thrown with a higher vertical velocity, and is pushed at the same exact height as in the first scenario, with the same horizontal velocity of 10m/s (this time though, the ball is not at it's max height so it still has an upward vertical velocity)

So they're asking how will the range vary in the two scenarios. If both the horizontal velocities are the same in both, then won't the range be the same? I thought that vertical and horizontal components are always independent from each other.

Their answer is that the Scenario 2 ball will have a larger range because it has a higher vertical velocity..... but I thought vertical velocity only influenced height and not the horizontal range?

Sorry that was long, thank you so much for any help!

 

[missdoctor]

You don't need those values to figure out the answer. They also don't give you those values anyway, you just have to make a comparison not calculate any specific numbers. This is exactly what it says:


Scenario 1:

The student at the base of a cliff throws a ball straight up, with enough initial speed that the ball just reaches the top of the cliff. When the ball reaches the top of the cliff, the second student standing at the edge of the cliff pushes the ball, giving the ball a horizontal velocity of 10 m/s.

Scenario 2:

This is the same in Scenario 1, except now the ball is thrown straight up with an initial speed greater than in Scenario 1. When the ball passes the top of the cliff, the student standing at the edge of the cliff gives the ball a horizontal velocity of 10m/s by pushing it.

The question asks to compare the range in Scenario 1 to the range in Scenario 2.

 

[Pons Asinorum]

I agree, I'm asking you to qualitatively tell me which ball is in the air longer, scenario 1 or scenario 2? You don't need to crunch numbers to know that the ball in scenario 2 is in the air longer than scenario 1. If it's in the air longer, and has the same horizontal velocity imparted on it by the guy on the cliff, isn't it qualitatively obvious that it has a longer range (distance traveled horizontally)?

You don't need those values to figure out the answer. They also don't give you those values anyway, you just have to make a comparison not calculate any specific numbers. This is exactly what it says:


Scenario 1:

The student at the base of a cliff throws a ball straight up, with enough initial speed that the ball just reaches the top of the cliff. When the ball reaches the top of the cliff, the second student standing at the edge of the cliff pushes the ball, giving the ball a horizontal velocity of 10 m/s.

Scenario 2:

This is the same in Scenario 1, except now the ball is thrown straight up with an initial speed greater than in Scenario 1. When the ball passes the top of the cliff, the student standing at the edge of the cliff gives the ball a horizontal velocity of 10m/s by pushing it.

The question asks to compare the range in Scenario 1 to the range in Scenario 2.

 

[missdoctor]

I agree, I'm asking you to qualitatively tell me which ball is in the air longer, scenario 1 or scenario 2? You don't need to crunch numbers to know that the ball in scenario 2 is in the air longer than scenario 1. If it's in the air longer, and has the same horizontal velocity imparted on it by the guy on the cliff, isn't it qualitatively obvious that it has a longer range (distance traveled horizontally)?

Hmm for some reason I'm not understanding that completely.. Like if you have a ball that you throw up vertically 10 m/s and let fall back down and hit the ground, and then you throw second ball up with a 20m/s vertical velocity, of course the second ball will be in the air for a longer time, but both balls will still land in the same spot on the ground.. it's just their vertical heights that would be different.

I think I'm having trouble with understanding how a more time in the air= further range... if the additional time in the air is due to the higher vertical velocity, then doesn't vertical velocity only contribute to the vertical height? How can vertical velocity lead to a horizontal distance increase?

I would've thought that the range would be the same for both because when the ball gets pushed, because regardless of what the vertical velocity was, it's changing direction and getting pushed horizontally. I think?

 

[fizzgig]

pons is trying to make the point that the X range is xvelocity*timeofflight

anything that keeps the ball in the air longer from the point you give it xvelocity will lengthen the xrange.

so you can look at the ycomponent situation from the time you hit the ball sideways.

 

[Dartmouth2005]

pons is trying to make the point that the X range is xvelocity*timeofflight

anything that keeps the ball in the air longer from the point you give it xvelocity will lengthen the xrange.

so you can look at the ycomponent situation from the time you hit the ball sideways.

That's it.

 

[missdoctor]

Ohh. And if they asked for the height and not the range, that would be vertical velocity times the time of flight?

I overlooked that time of flight x velocity equation. Okay well that equation explains why that's the answer but logically I still wonder how a vertical velocity increases horizontal range but I guess it's just the time that matters not the direction of the velocity. Thank you for the responses!

pons is trying to make the point that the X range is xvelocity*timeofflight

anything that keeps the ball in the air longer from the point you give it xvelocity will lengthen the xrange.

so you can look at the ycomponent situation from the time you hit the ball sideways.

 

[fizzgig]

it's not the vertical velocity directly, but vertical velocity gives you how long you're in the air. when you fire a projectile the vertical velocity gives you air hangtime and the horizontal velocity applies constantly until you hit the ground, independent of the vertical velocity itself.

the horizontal velocity is not being acted on by gravity (you fully separate the components), so you've got a constant (m/s) * (s) = m dimensional analysis going on.

the yvelocity is not constant because gravity is working on it. the height achieved from firing a projectile straight up, or the velocity achieved when an object is dropped from a certain height, can be found by v = sqrt(2gh)

 

[Pons Asinorum]

Ohh. And if they asked for the height and not the range, that would be vertical velocity times the time of flight?

I overlooked that time of flight x velocity equation. Okay well that equation explains why that's the answer but logically I still wonder how a vertical velocity increases horizontal range but I guess it's just the time that matters not the direction of the velocity. Thank you for the responses!

The way that it increases range is that the time value for horizontal motion can't be different than the time value for horizontal motion. TIME is what ties together the horizontal components (distance, velocity, acceleration) with the vertical components.

 

[grindtime1]

How is ball #2 in the air for a longer time than ball #1 when the question says that it (ball #2) is pushed horizontally from the exact same height as ball #1 but with a higher vertical velocity.

Doesn't this mean that ball #2 reached the point where it was pushed (the second boy's hand) in less time than ball #1?

 

[Rabolisk]

Did the ball move horizontally before it was pushed?

 

[Pons Asinorum]

I'm confused about how this question is still going around. Ok. You're sitting on your couch. You have a ball in each hand. You drop one straight down. At the exact same time, you toss the other ball straight up. They are released at the same height, it's just that one of them falls straight down, from 0 initial velocity, while the other flies up for a bit before gravity forces it back towards the ground. Which ball is in the air longer? Obviously it's the ball that started out flying up instead of straight down. The ball that had initial upward vertical velocity will be in the air longer, it will take longer to hit the ground. Now if two objects are given the same horizontal velocity, at the same time, and one of them stays in the air for longer, doesn't it make sense that it travels further than the other. Make a drawing or something. How is this question creating so much controversy on a forum designed to discuss issues with a physics-based entrance exam to a four-year postgraduate education. If people have made it through a year of high school and two semesters of college-based physics and still don't have the faintest grasp of projectile motion, then I despair over the condition of our education system. You may have your rantbox back now. Sorry.

How is ball #2 in the air for a longer time than ball #1 when the question says that it (ball #2) is pushed horizontally from the exact same height as ball #1 but with a higher vertical velocity.

Doesn't this mean that ball #2 reached the point where it was pushed (the second boy's hand) in less time than ball #1?

 

[Rabolisk]

Well some people just never had a great physics education.