A spacecraft starts in elliptical orbit JK (red solid curve) around some planet and transfers to elliptical orbit MN (blue solid curve). To do so, it changes its speed at K and inserts into the circular orbit KL (dashed green curve). At L, it changes speed again to insert into elliptical orbit LM (dashed magenta curve). Finally, at M, it changes speed to insert into the final orbit MN. Find all the changes in speed.

Acapacitor is storing energy of 3 joules with a voltage of 50 volts across its terminals. a second identical capacitor of the same value is storing energy of 1 joule. what is the voltage across the terminals of the second capacitor?

Simon is writing a story about an astronaut whose spacecraft has been boarded by space pirates. the astronaut has her lucky penny in her hand behind her back as the space pirates break into the control room. she has just locked the controls so that the ship is accelerating in the direction of the control room’s ceiling. simon wants the astronaut to use the penny to hit a button on the control panel to turn off the lights and escape. the button is located a short distance behind and below the astronaut’s hands. how should simon use the theory of relativity to describe what the astronaut must do in order to hit the button?

Aspring is used to stop a 50-kg package which is moving down a 20º incline. the spring has a constant k = 30 kn/m and is held by cables so that it is initially compressed 50 mm. knowing that the velocity of the package is 2 m/s when it is 8 m from the spring and neglecting friction, determine the maximum additional deformation of the spring in bringing the package to rest.