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.