Question

2: For this problem the heights are low enough that the acceleration due to gravity can be approximated as -g. (Note: even at low Earth orbit, such as the location of the International Space Station, the acceleration due to gravity is not much smaller then g. The apparent weightlessness is due to the space station and its occupants being in free-fall.)

A rocket is launched vertically from a launchpad on the surface of the Earth. The net acceleration (provided by the engines and gravity) is a1 (known) and the burn lasts for t1 seconds (known). Ignoring air resistance calculate:

a) The speed of the rocket at the end of the burn cycle.

b) The height of the rocket when the burn stops.

The main (now empty) fuel tank detaches from the rocket. The rocket is still propelled with the same acceleration as before due to the secondary fuel tank.

c) Calculate how long it takes for the main tank to fall back to the ocean back on the surface of the Earth in order to be recovered for next use.

d) Calculate the height of the rocket at the time when the tank hits the ocean.

e) At the time the main tank hits the ocean the secondary fuel tank runs out of fuel. Calculate the maximum height above the surface of the Earth that is reached by the rocket.

3: a) Consider a vector that points up and to the right at an angle of 45 degrees. Its magnitude is |A|. Write this vector in i-hat, j-hat notation.

b) A vector of similar magnitude points 30 degrees to the left of the positive y axis. Write this vector in i-hat, j-hat notation.

c) A vector of similar magnitude points 12 degrees to the left of the negative y axis. Write this vector in i-hat, j-hat notation.

Answer 1