How Does Earth's Longitude Affect Free Fall Equations?

In summary, to solve the given problem of free fall from a height h to the Earth's surface at a longitude φ, you can use projectile motion equations. By finding the initial velocity in x and y direction, and the angular speed, you can use the equation for position to get the result y(t)=(gωt^3cosφ)/3.
  • #1
Garunekk
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Homework Statement


Solve free fall from height h to the Earth´s surface in the place longitude φ. During solving, Consider gravitation acceleration as a constant for the whole trajectory, so g=constant. (consider a homogeneous gravity field) and variables which are including angular speed ω consider for much less then variables including gt. Consider h=100m and
φ=0 degree.
Result should be y(t)=(gωt^3cosφ)/3

Homework Equations


m(dv/dx)(dx/dt)=-2mωvsinφ
Fc=-2mωvsinφ
v=v0+gt
y=y0+v0t+1/2gt^2
ω=v/r

The Attempt at a Solution


Tried to make an differential equations, bude i can't get to my result.
 
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  • #2
I think to solve this kind of problem, it is better to use projectile motion equations. So, let's start by finding the initial velocity (v0) in x and y direction:v0x=0 (initial velocity in x-direction is zero)v0y=√2gh (initial velocity in y-direction)Now, we have to find the angular speed (ω):ω=v0/r (where r is the distance travelled by the object)Substituting the values:ω=√2gh/rNow, we can use the equation for position:y=y0+v0t+1/2gt^2Substituting the values:y=(gωt^3cosφ)/3
 

FAQ: How Does Earth's Longitude Affect Free Fall Equations?

What is "Free fall from height h"?

"Free fall from height h" refers to an object that is falling towards the ground from a specific height without any external forces acting upon it, such as air resistance or friction.

What is the acceleration of an object in free fall?

The acceleration of an object in free fall is approximately 9.8 meters per second squared, which is the acceleration due to gravity on Earth. This means that an object will increase its velocity by 9.8 meters per second every second as it falls towards the ground.

Does the mass of an object affect its free fall?

No, the mass of an object does not affect its free fall. All objects, regardless of their mass, will accelerate at the same rate due to gravity. This was famously demonstrated by Galileo's "thought experiment" of dropping objects of different masses from the Leaning Tower of Pisa.

What is the relationship between free fall and air resistance?

Air resistance, or drag, can affect the free fall of an object by slowing it down as it falls. This is because air resistance creates an upward force that opposes the force of gravity. As an object's velocity increases, so does the force of air resistance, resulting in a balance between the two forces. This is known as terminal velocity, where the object falls at a constant speed.

What factors can affect the free fall of an object?

The main factors that can affect the free fall of an object are the force of gravity, air resistance, and the initial height from which the object is dropped. Other factors such as the shape and mass distribution of the object can also play a role in its free fall. Additionally, the location and environment in which the object is falling can also affect its free fall.

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