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

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SUMMARY

The discussion focuses on calculating the maximum angle attained by a particle projected from Earth with an initial speed of 4 km/s. The relevant parameters include Earth's radius of 6400 km and gravitational acceleration of 9.8 m/s². Participants clarify the use of conservation of energy principles, correcting initial equations to ensure potential energy is included. The final equation discussed is 1/2{mv²} - GMm/R = -GMm/(R+H), which is essential for determining the altitude and angle of projection.

PREREQUISITES
  • Understanding of conservation of energy principles in physics
  • Familiarity with gravitational potential energy equations
  • Basic knowledge of projectile motion
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the conservation of mechanical energy in projectile motion
  • Learn about gravitational potential energy calculations
  • Explore the effects of initial velocity on projectile trajectories
  • Investigate the relationship between angle of projection and maximum height
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and projectile motion, as well as educators seeking to clarify concepts related to energy conservation in motion.

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?

[/B]
 
Last edited:
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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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