# Solving Newton's Laws Problem: Baseball Player & Runner

• ash312
In summary, a baseball player hits the ball with a velocity of 18.0m/s and a runner on third base starts running towards home plate which is 27.4m away. The time it takes for the ball to come down and the distance the runner covers in that time depends on the runner's speed. If the runner is running at 7.60 m/s, then the time and distance will be different compared to if he is running at a slower or faster speed.
ash312

## Homework Statement

A baseball player hits the ball straight up in the air with a velocity of 18.0m/s. As soon as the ball is hit, the runner on third base dashes toward the home plate. The distance between third base and home plate is 27.4m. Where will the runner be with reference to home plate when the ball returns to its initial height?

I am not sure

## The Attempt at a Solution

Dont understand how to start the solution

How long does it take for the ball to come down? How far does the guy run in this time? (Note that without the speed of the runner, it's impossible to answer this question. The answer will be very different if he's running at the speed of continental drift than if he's running at the speed of light)

The guy runs at 7.60 m /s

OK, so how long does it take for the ball to come down?

## 1. What are Newton's three laws of motion?

1. An object at rest stays at rest and an object in motion stays in motion with a constant velocity unless acted upon by an unbalanced force (Law of Inertia)

2. The force acting on an object is equal to the mass of the object multiplied by its acceleration (Law of Force and Acceleration)

3. For every action, there is an equal and opposite reaction (Law of Action and Reaction)

## 2. How do Newton's laws apply to a baseball player throwing a ball?

First, the player must overcome the initial inertia of the ball by applying a force to it. This force (the player's arm) is the unbalanced force that causes the ball to accelerate. According to Newton's second law, the acceleration of the ball is directly proportional to the force applied and inversely proportional to its mass. As the ball travels, it also experiences air resistance (a force in the opposite direction of its motion) and gravity (a force pulling it towards the ground). These forces must also be taken into account when determining the ball's trajectory.

## 3. How does a runner's motion demonstrate Newton's first law?

According to Newton's first law, an object at rest will stay at rest unless acted upon by an unbalanced force. Similarly, a runner will remain at rest until they apply a force (by pushing off the ground) to overcome their initial inertia and begin moving. Once they are in motion, they will continue moving at a constant velocity unless acted upon by an unbalanced force, such as friction or air resistance.

## 4. How does a runner's acceleration relate to Newton's second law?

Newton's second law states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. In the case of a runner, the force applied is their muscle power pushing against the ground, and the mass is their body weight. As the runner exerts more force, their acceleration will increase, and as their mass increases, their acceleration will decrease.

## 5. How does a baseball player's throwing motion demonstrate Newton's third law?

Newton's third law states that for every action, there is an equal and opposite reaction. In the case of a baseball player throwing a ball, the action is the force applied by the player's arm to the ball. The reaction is the equal and opposite force applied by the ball to the player's arm. This force causes the player's arm to move in the opposite direction of the ball, providing the necessary follow-through for the throw.

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