The max height the body reaches when this body is thrown verticaly upwards

In summary, the conversation discusses finding the maximum height of a vertically thrown body with a velocity of 5km/s, neglecting the impact of the atmosphere. The problem provides the radius of the Earth and the acceleration of gravity on the surface. The equations used are for kinetic energy, potential energy, and gravity. The final calculation should result in a height of 1553.4 meters, but the original attempt was incorrect and should be redone with proper unit conversions.
  • #1
mmoadi
157
0

Homework Statement



What is the maximum height that the body reaches when thrown vertically upwards from the surface of the Earth at a velocity of 5km/s, if we neglect the impact of the atmosphere? The radius of the Earth is r= 6400km; the acceleration of gravity on the surface is g = 10 m/s².

Homework Equations



KE= mv²/2
PE= mgh

The Attempt at a Solution



KE + PE = PE’

(mv²/2) – (mM/r)G = -(mM/r+h)G

F(gravity)= mg
f = (mM/ r²)G

mg = (mM/ r²)G
g= MG/ r²) → MG = g r²

h= [g r² / rg/r – v0²/2] – r
h= 1553.4 m

Are my calculations correct?
 
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  • #2
Your answer is too low by a factor of 1000. Redo the calculation and pay attention to the powers of 10 that you put in. Be sure to convert all kilometers to meters.
 
  • #3


I cannot validate the accuracy of your calculations without knowing the specific values of the variables used. However, your approach and use of relevant equations are correct. To confirm the accuracy of your calculations, it would be helpful to provide the specific numerical values used for each variable, including the mass of the body and the mass and radius of the Earth. Additionally, it would be beneficial to show your work and any assumptions made during the calculation process. This will allow for a more thorough evaluation of your solution.
 

What is the max height reached when an object is thrown vertically upwards?

The maximum height an object reaches when thrown vertically upwards is dependent on various factors such as initial velocity, air resistance, and gravity. It can be calculated using the formula:

h = (v2 / 2g), where h is the height, v is the initial velocity, and g is the acceleration due to gravity.

Does the mass of the object affect the maximum height reached?

Yes, the mass of the object does affect the maximum height reached. Heavier objects will have a lower maximum height because they require more force to overcome the gravitational pull. However, in a vacuum where air resistance is negligible, the mass of the object does not affect the maximum height reached.

How does air resistance affect the maximum height reached?

Air resistance can significantly affect the maximum height reached by an object. As the object moves upwards, it experiences a force of air resistance in the opposite direction of its motion. This force slows down the object and reduces its maximum height. In a vacuum, where there is no air resistance, the object will reach a higher maximum height.

Is the maximum height reached the same as the final height?

No, the maximum height reached is not the same as the final height. The maximum height is the highest point the object reaches in its trajectory, and it occurs when the object's velocity becomes zero. The final height is the height at which the object lands after its motion is complete. In the absence of air resistance, the maximum height and final height will be the same.

How does the angle at which the object is thrown affect the maximum height reached?

The angle at which the object is thrown can affect the maximum height reached. When an object is thrown at an angle less than 90 degrees, its initial velocity is divided into horizontal and vertical components. The vertical component determines the maximum height reached, while the horizontal component determines the distance traveled. Therefore, the maximum height reached will be greater when the angle of throw is closer to 90 degrees.

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