# Starship + 2 different planets?

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In summary, the problem involves a ball rolling off a table inside a starship on Earth and then being repeated on another planet, Planet X, with the same initial speed but different distances traveled. The solution involves using the four basic equations of motion and finding an expression for the range of the projectile, taking into account the different acceleration due to gravity on Planet X. This is a projectile motion problem and requires writing expressions for horizontal and vertical positions at any time, eliminating time, and finding the dependence of the range on initial speed and vertical height.
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Starship + 2 different planets?

## Homework Statement

The problem from my textbook is:
Inside a starship at rest on earth, a ball rolls off the top of a horizontal table and lands a distance D from the foot of the table. This starship now lands on the unexplored Planet X. The commander, Captain Curious, rolls the same ball off the same table with the same initial speed as on Earth and finds that it lands a distance 2.76D from the foot of the table. What is the acceleration due to gravity on Planet X?

## Homework Equations

The 4 basic equations of motion:
V=Vi + a x delta t
S=Si + Vi x delta t + 1/2at^s
S=Si + 1/2(V+Vi)delta t
V^2= Vi^2 + 2a(S-Si)

## The Attempt at a Solution

I know the initial velocity is the same in both cases, I figure you have to substitute the initial velocity in one with an equation with the acceleration on earth. I'm kind of lost from this point.
What I really need is some one to explain how to solve it.

Last edited:

This is a projectile motion problem. You need to find an expression for the range of the projectile given that it has initial velocity v0 only in the horizontal direction and starts at height h above ground. Can you find such an expression?

I'd have to rearrange equations and substitute them into one another and I wouldn't know where to start.

Start by writing expressions for the horizontal position of the ball at any time t and for the position of the ball above ground at any time t. Eliminate the time and find an expression giving the dependence of the range on the vertical height and the initial speed.

I would approach this problem by first identifying the known and unknown variables. We know the distance D on Earth and 2.76D on Planet X, and we are trying to find the acceleration due to gravity on Planet X.

Next, I would use the equation S=Si + Vi x delta t + 1/2at^2 to solve for the acceleration on Earth. We know the initial velocity (Vi) is the same in both cases, and we can plug in the known distance D and the time it takes for the ball to land (which is the same on both Earth and Planet X). This will give us the acceleration due to gravity on Earth.

Once we have the acceleration on Earth, we can use the equation V^2= Vi^2 + 2a(S-Si) to solve for the acceleration on Planet X. We know the initial velocity and the distance (2.76D) on Planet X, and we can plug in the acceleration we found on Earth. This will give us the acceleration due to gravity on Planet X.

It's important to note that this solution assumes the same initial conditions and no external forces acting on the ball. If there are any other factors at play, the results may vary.

## 1. What is a starship and how does it travel to different planets?

A starship is a vehicle designed for space travel, typically powered by advanced propulsion systems. It uses the principles of physics, such as thrust and gravity, to navigate through space and reach different planets.

## 2. Can a starship travel to any planet in the universe?

Technically, yes, a starship has the capability to travel to any planet in the universe. However, the distance and time required to reach some planets may make it impractical or impossible with current technology.

## 3. How do scientists choose which planets to explore with a starship?

Scientists consider a variety of factors when choosing which planets to explore with a starship, such as the planet's distance from Earth, its size and composition, and the potential for finding signs of life or habitability.

## 4. Can a starship land on a planet and return to Earth?

Yes, depending on its design and capabilities, a starship can land on a planet and return to Earth. This would require advanced navigation systems, as well as the ability to withstand the various conditions of different planets.

## 5. How does the discovery of new planets through starship exploration benefit scientific research?

The discovery of new planets through starship exploration allows scientists to expand their understanding of the universe and potentially discover new resources or environments that can contribute to our knowledge of space. It also provides opportunities for further research and potentially finding signs of extraterrestrial life.

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