1. A straight river flows east at a speed of 20 mi/h. A boater starts at the south shore of the river and heads in the direction which is 60° to the south shore. The motorboat has a speed of 20 mi/h relative to the water. (a) Express the velocity of the river as a vector in component form. (b) Express the velocity of the motorboat relative to the water as a vector in component form. (c) Find the true velocity of the motorboat. (d) Find the true speed of the motorboat. (e) Find the true direction of the motorboat (as a bearing).
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Parts A-C
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