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## Escape Velocity

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**Cont’d**• Consider a projectile of mass m, leaving the surface of a planet (or some other astronomical body) with escape velocity v. It has a kinetic energy k given by:**Cont’d**• The projectile also has potential energy U given by:**Cont’d**• When the projectile reaches maximum height v=0 since v(instantaneous velocity) is the derivative of altitude with respect to time. Therefore k = 0. Also as rthe potential energy goes to zero. Based on the principal of conservation of energy , the total energy of the projectile at the planet’s surface must also have been zero. Therefore,**Escape speed**• The escape speed does not depend on the direction in which a projectile is fired.However, attaining the speed is easier if the projectile is fired in the direction the launch site is moving as Earth rotates about its axis.**Escape speed**Rockets are launched eastward at Cape Conaveral to take advantage of the Cape’seastward speed of 1500km/h.