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Also, 2 balls are launched upwards from the same spot but at different angles. the both will have the same max height. which ball goes further?

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- Thread starter bigdaddy
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Also, 2 balls are launched upwards from the same spot but at different angles. the both will have the same max height. which ball goes further?

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Show some work, please.

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A for the second one, i think that the ball with the greater angle will fall shorter than the ball with a less angle. the inital velocities are different i know that. Maybe i am thinking to much in the common sense part? i am completely confused about this one. I dont need answers i just need direction. As for both these questions, there are no numbers involved.

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A ball (A) is launched straight down from a cliff while another (B) is launched straight up from the floor of the cliff. The final velocity for ball A is the inital velocity for ball b. Where will they cross paths? Up high, in the middle or down low?

Also, 2 balls are launched upwards from the same spot but at different angles. the both will have the same max height. which ball goes further?

what i think is happening is that on question 1, they are actually meeting in the middle since the intial velocity of the ball thrown from the floor is at the same final velocity of the ball dropped, do i make sense? the ball thrown from the floor is decreasing velocity while the ball dropped increases.

A for the second one, i think that the ball with the greater angle will fall shorter than the ball with a less angle. the inital velocities are different i know that. Maybe i am thinking to much in the common sense part? i am completely confused about this one. I dont need answers i just need direction. As for both these questions, there are no numbers involved.

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Dick

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rl.bhat

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In the second one, high speed low angle and low speed high angle can have same maximum height. The range will be more in the first case.

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Dick

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As for both these questions, there are no numbers involved.

That does not mean you can't use variables to represent things like speeds, heights, angles. Doing physics without mathematics is a bit like playing a video game without an interface. It just doesn't make sense.

How much time does it take for the dropped ball to fall half the distance? For the thrown ball to rise half the distance? Are these times the same, or different?what i think is happening is that on question 1, they are actually meeting in the middle since the intial velocity of the ball thrown from the floor is at the same final velocity of the ball dropped, do i make sense? the ball thrown from the floor is decreasing velocity while the ball dropped increases.

The greater angle with respect to what? Vertical or horizontal?A for the second one, i think that the ball with the greater angle will fall shorter than the ball with a less angle. the inital velocities are different i know that. Maybe i am thinking to much in the common sense part? i am completely confused about this one. I dont need answers i just need direction.

You might find it helpful to draw a picture for both problems.

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Moderator: This thread should be merged with https://www.physicsforums.com/showthread.php?t=239703".

*bigdaddy: prove this.* If object A takes time *t* to fall a height *h*, how far will it have fallen during half of this time?

Presumably there is gravity given that there are an initial and final velocity. Here is an easy way to look at it: They will meet in exactly half the time it takes for A to fall to the bottom of the cliff (or for B to rise to the top of the cliff).Ireally can't think of a nice way to present it. But so far I seem to be finding that they will only meet in the middle if g=0.

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Dick

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(a) is just as obvious to me if you realize they must meet at the midpoint in time rather than the midpoint in space. The qualitative answer falls out immediately. This looks like a qualitative physics problem to me, so it might well be real.

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I have to say on question 2, the ball that goes the farthest is the one with the greater initial x velocity. The angles are wrt the horizontal plane.

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Dick

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I have to say on question 2, the ball that goes the farthest is the one with the greater initial x velocity. The angles are wrt the horizontal plane.

That's exactly right. If you work out the extreme cases g~0 v0 large, you find the ratio is almost 1/2. If g is large and v0 small, the ratio is almost 3/4. So yes, upper half. I hadn't thought about g<0 case but what you say makes sense.

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The way to solve this problem qualitatively is to realize that the balls must meet at the midpoint

I can see people coming up with different answers for the second question because some will talk about angle from the vertical and others, angle from the horizontal, and do so without realizing they aren't talking about the same thing. The ambiguity goes away as soon as a reference line is established. The ambiguity also vanishes if the discussion is couched in terms of horizontal velocity component instead of angle.

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