# Free-Falling Body Question

• NDiggity
In summary, the problem involves a man throwing a ball from the top of a 25m building with an initial velocity of 12 m/s. Another man catches the ball at the bottom of the building, 31m away. To find the average speed of the man catching the ball, kinematics equations are used with an acceleration of -9.8 m/s^2 and a velocity of 0. After some calculations, a negative value appears in the equation, but this is due to using displacement instead of distance. By correcting the sign convention, the correct value for time can be found and used to calculate the average speed of the man catching the ball. Another approach is to solve the problem in one step using the quadratic formula

## Homework Statement

A guy on the top of a 25m building throws a ball upwards with a initial vel of 12 m/s. A guy 31 m from the building catches it at the bottom of the building. What must be the average speed of the guy to catch it at the bottom.

## Homework Equations

Using the Kinematics equations, and using acceleration = -9.80 m/s^2 and v= 0, I find the time up to be 1.22s. Then I find the distance up as 7.35m. Then I find the time it takes to fall down by adding 7.35 to 25 m, using initial velo as 0, and acceleration. But I get a negative on one side in this equation, x = vint(t) + (1/2)(a)(t^2). What am i doing wrong?

I know once I get this time I add it to 1.22s. Then I believe I use v=d/t and plug in 31m for distance and the total time.

Hi NDiggity,

NDiggity said:

## Homework Statement

A guy on the top of a 25m building throws a ball upwards with a initial vel of 12 m/s. A guy 31 m from the building catches it at the bottom of the building. What must be the average speed of the guy to catch it at the bottom.

## Homework Equations

Using the Kinematics equations, and using acceleration = -9.80 m/s^2 and v= 0, I find the time up to be 1.22s. Then I find the distance up as 7.35m. Then I find the time it takes to fall down by adding 7.35 to 25 m, using initial velo as 0, and acceleration. But I get a negative on one side in this equation, x = vint(t) + (1/2)(a)(t^2). What am i doing wrong?

I assume you used a= -9.8 m/s^2 like you did before. But what number did you use for x in that equation? If the distance from the top to the ground is (7.35 + 25) = 32.35, then x is not 32.35. (Close, but not quite.) Remember that the x in that equation is displacement, not distance. What do you get?

You aren't doing anything wrong. Except that x in your formula is a displacement from the original position. With your sign conventions, that IS -(7.35+25)m. Now there's a negative on both sides. Just go ahead and solve it as you intended. Think about what the signs mean in terms of the problem and your coordinates.

Ahh, so since I was using up as positive, displacement would be -32.35 since the ball is going down. Thank you both so much!

Last edited:
An alternative way is that you could actually find the time in one step, from the initial throw to the ball hitting the ground (insted of using three equations). Displacement is -25, initial velocity is +12, so:

$$(-25)= (+12) t + \frac{1}{2}(-9.8) t^2$$

Of course you'll have to use the quadratic formula to find t doing it this way, and you'll keep the positive answer.

## What is a free-falling body?

A free-falling body is an object that is only affected by the force of gravity as it falls through the air or a vacuum.

## What is the acceleration of a free-falling body?

The acceleration of a free-falling body is approximately 9.8 meters per second squared, or 32.2 feet per second squared, regardless of the mass or size of the object.

## Does air resistance affect the motion of a free-falling body?

Yes, air resistance or air friction can affect the motion of a free-falling body. As an object falls, it pushes against air molecules, which creates a force in the opposite direction of motion. This force, called air resistance, can slow down the object's acceleration.

## How does the height of a free-falling body affect its velocity?

The height of a free-falling body does not affect its velocity. However, the higher the object is dropped from, the longer it will take to reach the ground.

## What is the difference between free fall and terminal velocity?

Free fall is the motion of an object that is only affected by the force of gravity. Terminal velocity is the maximum velocity that a free-falling object can reach when air resistance balances out the force of gravity. In other words, it is the point at which the object stops accelerating and falls at a constant speed.