# How Does Gravity on Planet X Compare to Earth's?

• J89
In summary, a ball rolled off a horizontal table on a starship at rest on Earth and landed at a distance D from the foot of the table. When the starship landed on Planet X, the commander rolled the same ball with the same initial speed and found that it landed at a distance of 2.76D from the foot of the table. To find the acceleration due to gravity on Planet X, the kinematic equation x= x(initial) + v(initial)t + .5at^2 can be used. Assuming a velocity of 1 m/s and a time of 1.52 sec, the acceleration due to gravity on Planet X is approximately 1.3 m/s^2.
J89

## Homework Statement

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

## Homework Equations

x=(V0cosa0)t
y=(V0sina0)t - 1/2gt^2
Vx=V0cosa0
Vy=V0sina0-gt

## The Attempt at a Solution

I made up the initial speed since it was not given and assumed a time. and used y=(V0sina0)t - 1/2gt^2...came out completely wrong :(

I made up a situation as well. I let the height of the table = 1.5 m and the horizontal velocity of the ball be 1 m/s. I then used the kinematic equation x= x(initial) + v(initial)t + .5at^2. I analyzed the vertical data for Earth to see how long it was in the air, and got .55 sec. I then used the same kinematic for the x direction, except this time I used that time to see how far it went. I got .55 m. This is our "D" value. So, on planet x it travel 2.76 D. We get 1.52 m for the distance traveled for the ball. Since I choose a velocity horizontally of 1 m/s, that ball on planet x traveled for 1.52 sec before hitting the ground. Now, analyze the y direction using yet again the same kinematic and we can solve for a, or the acceleration due to gravity on planet x. Assuming i didn't mess up anything, it should be 1.3 m/s^2.

I would approach this problem by first identifying the relevant equations and variables. In this case, the equations for projectile motion in the x and y directions are relevant, as well as the acceleration due to gravity (g). The variables that we know are the distances D and 2.76D, and the initial speed (V0) is the same on both Earth and Planet X.

Next, I would use the given information to set up a system of equations. Since we know that the initial speed and angle of launch are the same on both Earth and Planet X, we can set the equations for the y-direction equal to each other:

(V0sina0)t - 1/2gt^2 = (V0sina0)t - 1/2gt^2

From this, we can see that the only difference between the two scenarios is the value of g. So, we can set up a proportion:

D/g on Earth = 2.76D/g on Planet X

Solving for g on Planet X, we get:

g = (2.76D/g)(D/2.76D) = 2.76g

Therefore, the acceleration due to gravity on Planet X is 2.76 times the value of g on Earth. This makes sense, as the planet could have a higher mass or different composition, leading to a stronger gravitational pull.

## What is projectile motion?

Projectile motion is the motion of an object through the air, under the influence of gravity. It is a type of motion that occurs when an object is thrown or launched into the air and then falls back to the ground due to the force of gravity.

## What factors affect projectile motion?

The factors that affect projectile motion include the initial velocity, angle of launch, air resistance, and gravity. These factors can change the trajectory and distance of the projectile.

## What is the difference between horizontal and vertical velocity in projectile motion?

Horizontal velocity refers to the speed at which the object is moving parallel to the ground, while vertical velocity is the speed at which the object is moving in an upward or downward direction. In projectile motion, the vertical velocity is affected by gravity, while the horizontal velocity remains constant.

## How do you calculate the range of a projectile?

The range of a projectile is the horizontal distance it travels before hitting the ground. It can be calculated using the formula R = (v02sin(2θ))/g, where v0 is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

## What are some real-life examples of projectile motion?

Some real-life examples of projectile motion include throwing a ball, launching a rocket, kicking a soccer ball, and shooting a basketball. These all involve an object being launched into the air and falling back to the ground due to the force of gravity.

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