# Solving a Physics Problem: Falling Ball from Tabletop

• lauriecherie
In summary, a ball is rolled horizontally off a tabletop 1.40 m high and strikes the floor 1.56 m away from the table edge. The time it was in the air can be determined using the equation y = 1/2*g*t^2, with a correct answer of 0.53 seconds. To find the speed of the ball at the instant it left the table, the equation t = SQR(2s / a) can be used, where a is the acceleration due to Earth's gravity (9.8 m/s^2) and s is the distance traveled (1.56 m). The correct velocity is then calculated by dividing the horizontal distance by the time.
lauriecherie

## Homework Statement

A ball rolls horizontally off the edge of a tabletop that is 1.40 m high. It strikes the floor at a point 1.56 m horizontally away from the table edge. (Neglect air resistance.)
(a) How long was the ball in the air?
_____ s

(b) What was its speed at the instant it left the table?
______ m/s

## The Attempt at a Solution

Is 3.12 s correct? And is 30.576 m/s correct? Seems awfully fast...?

How do you determine the time?

y = 1/2*g*t2

Ok the correct answer for time is .53 s

lauriecherie said:
Ok the correct answer for time is .53 s

That's what I get.

That is correct so far. Now, how would you determine the speed it was going at when it left the table?

It may help to think in individual x and y coordinates for this part.

t = SQR(2s / a)

where,

a = acceleration (in m/s^2) per Earth’s gravity = 9.8 m/s^2
s = distance (in meters)
t = time (in seconds)
v = velocity (in m/s)
SQR = square root of the product within the parenthesis

Once you’ve derived the correct time (t), divide the 1.56 meter horizontal distance achieved by the ball, by the time (t) to derive the correct velocity (v):

1.56 meters / t = velocity (in m/s)

## 1. How do I calculate the time it takes for a ball to fall from a tabletop?

The time it takes for a ball to fall from a tabletop can be calculated using the equation t = √(2h/g), where t is the time in seconds, h is the height in meters, and g is the acceleration due to gravity (9.8 m/s²).

## 2. What is the initial velocity of the ball when it falls from a tabletop?

The initial velocity of the ball can be calculated using the equation v = √(2gh), where v is the initial velocity in meters per second, g is the acceleration due to gravity, and h is the height in meters.

## 3. How do I determine the final velocity of the ball when it reaches the ground?

The final velocity of the ball when it reaches the ground can be calculated using the equation v = √(2gh), where v is the final velocity in meters per second, g is the acceleration due to gravity, and h is the height in meters.

## 4. Is the mass of the ball a factor in calculating its acceleration?

Yes, the mass of the ball is a factor in calculating its acceleration. The equation for acceleration is a = F/m, where a is the acceleration in meters per second squared, F is the net force acting on the ball, and m is the mass of the ball in kilograms. Therefore, a heavier ball will have a greater acceleration than a lighter ball when dropped from the same height.

## 5. What is the effect of air resistance on the falling ball?

Air resistance can have a significant effect on the falling ball, especially if it is dropped from a great height. As the ball falls, it will experience an upward force due to air resistance, which will decrease its acceleration. This means that the ball will take longer to reach the ground and will have a lower final velocity. To account for air resistance, we can use the equation v = √(2gh(1-e^(-k/m)t)), where k is a constant representing the air resistance and t is the time in seconds.

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