What is the minimum energy needed to lift a 1.0-kg rocket to a height of 200 km and to give it a speed of 8.0 km/s at that height? (Neglect air resistance and the small decrease in g over that
Distance.)
A) 34 J
B) 34 GJ
C) 34 TJ
D) 34 kJ
E) 34 MJ

Question

Quizplus · Accepted Answer

To find the minimum energy needed, we need to calculate both the potential energy (PE) gained by lifting the rocket to a height of 200 km and the kinetic energy (KE) it has due to its speed of 8.0 km/s at that height. The potential energy gained is given by PE = mgh, where m is the mass (1.0 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height (200,000 m, since we need to convert kilometers to meters). So, PE = 1.0 kg * 9.8 m/s^2 * 200,000 m = 1,960,000 J or 1.96 MJ.The kinetic energy is given by KE = 1/2 mv^2, where m is the mass (1.0 kg) and v is the speed (8,000 m/s, converting km/s to m/s). So, KE = 0.5 * 1.0 kg * (8,000 m/s)^2 = 32,000,000 J or 32 MJ.The total energy required is the sum of PE and KE, which is 1.96 MJ + 32 MJ = 33.96 MJ, which rounds to 34 MJ.

What Is the Minimum Energy Needed to Lift a 1