What Is the Maximum Angle Attained by a Particle Projected from Earth?

AI Thread Summary
A particle is projected from Earth with an initial speed of 4 km/s, and the goal is to determine the maximum angle it attains. The relevant equations involve conservation of energy, specifically relating kinetic and potential energy. Initial attempts at formulating the equation included errors, particularly in combining kinetic energy with gravitational force. Corrections were suggested, emphasizing the need to focus on potential energy and clarify the distinction between altitude and angle. The discussion highlights the importance of accurately applying conservation principles to solve the problem.
harambe
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Homework Statement


A particle is projeccted from the surface of the Earth with an initial speed of 4km/s.Find the maximum angle attained by the particle.Radius of the earth=6400km and g=9.8m/s2

Homework Equations



KE1+U1=KE2+U2
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The Attempt at a Solution



So I tried to proceed by this method

1/2{mv2} - GMm/R=-GM/(R+H)

Is my equation right?

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You have the kinetic energy and the force/mass (which is the local acceleration due to gravity) in the same equation. So yes, your equation is incorrect. You are looking for the conservation of the total energy.
 
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Oops .I had to use potential energyIs it right now
 
If you are trying to calculate the altitude above the surface of the Earth, then almost. Take another look at the RHS of your equation..
 
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harambe said:
Find the maximum angle
Angle? Altitude maybe?
As Dr Dr news mentions, you have a typo in your equation.
 
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1/2{mv2} - GMm/R=-GMm/(R+H)
Is this correct
 
That looks good.
 
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