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# Escape Speed

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Escape Velocity

• Escape velocity is the minimum velocity that a body must attain to escape the gravitational field of the earth.

• Suppose if we throw a ball,it will fall back. This is happening due to the force of gravitation exerted on the ball by the surface of the earth due to which the ball is attracted towards the surface of the earth.

• If we increase the velocity to such an extent that the object which is thrown up will never fall back.This velocity is known as escape velocity.

• Ball is thrown up but it falls down because of force of gravitation.
• The same ball is thrown with a velocity that it escapes the force of gravitation of earth and does not come back. This velocity is known as escape velocity.
• Mathematically:-

Suppose we throw a ball and the initial velocity of the ball is equal to the escape velocity such that ball never comes back.

Final Position will be infinity.

At Final Position: At Infinity

Total Energy (oo) = kinetic Energy (oo) + Potential Energy (oo)

Kinetic Energy (oo) = 1/2"mv"_f^2 where V_f=final velocity

Potential Energy (oo) = -"GMm"/"r" + V_o

Where M=mass of the earth, m= mass of the ball,

Vo=Potential energy at surface of earth, r=oo r= distance from the centre of the earth

therefore potential energy(oo)= 0

Total Energy(oo)=1/2"mv"_f^2        ...(1)

• At initial Position:

"E"=1/2"mv"_i^2

"E"=-("GMm")/(("R"_e + "h"))+"V"_o

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