# Motion problem? (Ball is thrown upward)

In summary, the conversation is about solving a physics problem involving acceleration and time. The person attempted to use the formula "Distance = Speed x Time" to find the speed, but it was incorrect because the motion is accelerated. The other person suggests only using formulas with acceleration and considering only the falling part of the problem.

## The Attempt at a Solution

I assumed that it was the same time going up as it was going down, and thus I had:

V(initial) = 0 m/s
a = -9.81 m/s^2
t = .84 seconds

And to solve for speed, I used the Distance = Speed x Time, thus Speed = Distance/Time... and used the Displacement = 1/2(V(initial) + V(final))*time to find the "distance", and then divide it by .84 seconds... but this was incorrect? ):

"Distance = Speed x Time" does not apply because the motion is accelerated. Only use formulas with acceleration in them. Your insight that the time to fall is equal to the time to rise may well simplify the problem - consider only the falling part.

## 1. What is the formula for calculating the height of a ball thrown upward?

The formula for calculating the height of a ball thrown upward is h = v0t - 1/2gt2, where h is the height, v0 is the initial velocity, g is the acceleration due to gravity, and t is the time elapsed.

## 2. How do you calculate the maximum height reached by a ball thrown upward?

The maximum height reached by a ball thrown upward can be calculated using the formula hmax = v02/2g, where hmax is the maximum height, v0 is the initial velocity, and g is the acceleration due to gravity.

## 3. What is the relationship between the initial velocity and the maximum height reached by a ball thrown upward?

The initial velocity and the maximum height reached by a ball thrown upward have a direct relationship. This means that as the initial velocity increases, the maximum height also increases, and vice versa.

## 4. How does air resistance affect the motion of a ball thrown upward?

Air resistance can have a significant effect on the motion of a ball thrown upward. As the ball travels through the air, it experiences a force of air resistance that opposes its motion. This force can decrease the ball's initial velocity and therefore decrease its maximum height reached.

## 5. Is the motion of a ball thrown upward considered free fall?

Yes, the motion of a ball thrown upward is considered free fall because it is only under the influence of the force of gravity. However, during its upward motion, the ball's velocity and acceleration are in opposite directions, making it a type of non-uniform motion known as projectile motion.

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