In: Physics
A test ballistic missile, having a mass of 500 kg, is launched straight up into the air from the Earth’s surface with an initial velocity of 0.6 km/s. The missile reaches some height, stops, and then descends back to Earth (without a parachute).
a) What were the missile’s initial kinetic energy, potential energy, and total mechanical energy at the exact time of its launch (all in units of joules)?
b) What were the missile’s kinetic energy, potential energy, and total mechanical energy when it reached its greatest height (all in units of joules)? Ignore the effects of air resistance.
c) How high did the missile climb before it began to descend (in metres AND feet)? Ignore the effects of air resistance.
d) How long does the missile take to drop from its highest height back to the ground (in seconds)?
In this problem we will use the concept of conservation of mechanical energy which states that total mechanical energy of a system will always conserve. At the time of launch the height of the missile with respect to ground is zero and so its potential energy is also zero , so its total mechanical energy = kinetic energy. At highest point the velocity of the missile is zero so kinetic energy is zero ,and total mechanical energy = potential energy.