Final answer:
The speed of the rocket when it is 255 m above the surface of the Earth can be calculated using the principle of conservation of mechanical energy.
Step-by-step explanation:
The speed of the rocket when it is 255 m above the surface of the Earth can be calculated using the principle of conservation of mechanical energy. At this height, the only form of energy the rocket has is its potential energy. The potential energy can be converted to kinetic energy, which is given by the equation:
KE = (1/2)mv^2
where m is the mass of the rocket and v is its speed. The potential energy at 255 m can be calculated as:
PE = mgh
where g is the acceleration due to gravity and h is the height.
By equating the potential and kinetic energies, we can find v:
KE = PE
(1/2)mv^2 = mgh
v^2 = 2gh
v = sqrt(2gh)
Substituting the values of g = 9.8 m/s^2 and h = 255 m, we can calculate v.
v = sqrt(2 * 9.8 * 255)
v ≈ 69.6 m/s