Comparing the Speeds of Thrown Balls at Ground Level

In summary, the problem is to determine which ball, thrown straight up and straight down from the top of a building with the same speed, has the greater speed when it reaches the ground. The student's attempt at a solution is that the ball thrown straight up will have a greater speed due to having a longer acceleration time. However, this answer is incorrect and the problem can be solved conceptually without using mathematical equations.
  • #1
Gurasees
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1
Problem Statement

From the top of the building if we throw one ball straight up with speed v and one ball straight down with the same speed v, then which ball has the greater speed when it reaches the ground?

The attempt at a solution


I think the ball which is first thrown straight up will have greater speed (than the ball which is thrown straight down) when they reach the ground because it has had accelerated for longer time than the second ball.
 
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  • #2
Gurasees said:
Problem Statement

From the top of the building if we throw one ball straight up with speed v and one ball straight down with the same speed v, then which ball has the greater speed when it reaches the ground?

The attempt at a solution


I think the ball which is first thrown straight up will have greater speed (than the ball which is thrown straight down) when they reach the ground because it has had accelerated for longer time than the second ball.
You deleted the part of the Homework Template that asks for the "Relevant Equations" -- you should use the equation for the vertical motion of that mass to figure this problem out. The answer may not be intuitive to you yet, so it's best to do the math...
 
  • #3
Probably you should not guess, but try to formulate the problem mathematically. Do you have any idea which formulas you could use to solve it? If you are not familiar with these kind of calculations yet I suggest to start easy. What's the velocity of the ball, when touching the ground if ##v_0=0##?
 
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  • #4
Without doing the actual calculations, can you describe how the first ball's velocity changes going up and compare that with how its velocity changes coming back down to you at the top of the building? Then you can compare that ball continuing down from the top of the building with the second ball you throw down from the same point.
 
  • #5
In case you haven't figured it out yet from the other responses, your answer, OP, was wrong.
 
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  • #6
stockzahn said:
Probably you should not guess, but try to formulate the problem mathematically. Do you have any idea which formulas you could use to solve it? If you are not familiar with these kind of calculations yet I suggest to start easy. What's the velocity of the ball, when touching the ground if ##v_0=0##?

Actually, as @FactChecker has implied, this can be solved conceptually without having to resort to solving the mathematics.

@Gurasees : For the ball that you tossed vertically upwards, what do you think its speed will be on the way down when it passes its original location?

Zz.
 
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  • #7
ZapperZ said:
Actually, as @FactChecker has implied, this can be solved conceptually without having to resort to solving the mathematics.
But I LIKE the math! :partytime:
 
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  • #8
berkeman said:
But I LIKE the math! :partytime:

Doesn’t mean you can’t solve it that way, but it can be solved without it.

This is the type of question that I give the students when we employ peer-instruction technique.

Zz.
 
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Related to Comparing the Speeds of Thrown Balls at Ground Level

1. What is acceleration due to gravity?

Acceleration due to gravity is the rate at which an object falls towards the Earth due to the pull of gravity. It is typically denoted as "g" and has a constant value of 9.8 meters per second squared (m/s^2) near the Earth's surface.

2. How is acceleration due to gravity calculated?

Acceleration due to gravity can be calculated using the formula a = g = F/m, where "a" is the acceleration, "g" is the gravitational constant, "F" is the force of gravity, and "m" is the mass of the object.

3. Does acceleration due to gravity vary on different planets?

Yes, acceleration due to gravity varies on different planets depending on their mass and radius. The larger the mass and radius of a planet, the stronger the pull of gravity and therefore, the higher the acceleration due to gravity will be.

4. How does altitude affect acceleration due to gravity?

The acceleration due to gravity decreases as altitude increases. This is because as an object moves farther away from the Earth's surface, the pull of gravity becomes weaker. However, this effect is only significant at large distances from the Earth's surface, such as in space.

5. Can the acceleration due to gravity be negative?

Yes, the acceleration due to gravity can be negative. This occurs when an object is moving towards the Earth and the acceleration is in the opposite direction of the object's motion. This is commonly seen when an object is thrown upwards and begins to fall back towards the Earth.

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