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2017-06-05 Intermediate


A rocket, initially at rest in deep space, starts its thrusters, which then burn and eject fuel at a uniform rate to provide constant thrust to the rocket.

How does the speed of the rocket vary with time until all of the fuel is exhausted?

A ball is thrown vertically upwards with a velocity of 2 m/s.\SI[per-mode=symbol]{2}{\meter\per\second}. It is seen at height hh twice.

Find the sum of the times, measured in seconds from the moment the ball is thrown, at which it is seen at height hh.

Details and Assumptions:

  • Take g=10 m/s2g=\SI[per-mode=symbol]{10}{\meter\per\second\squared}.
  • Neglect air resistance.

Does there exist a power of 2 whose last 4 digits are all identical?

Note: nn is a positive integer.








In the diagram above, ABCDABCD is a square, NC=2DN,NC = 2DN, and NMB=MBC.\angle NMB = \angle MBC.

If MDNMDN is not a degenerate triangle (that is, its area is non-zero), what is tanABM?\tan \angle ABM?


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