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Need help in this vector math question….?
A ship is moving with a constant speed of 10(√ 5 ) km/h parallel to the vector i + 2j and is initially at the origin.
Let the velocity of the ship be V
The solution:
V= 10(√ 5)[ (√ 5)^( -½)] (i + 2j )
Why is the solution so?
4 Answers
- 1 decade agoFavorite Answer
Velocity, as u know, is a vector. Thus it has magnitude and direction. Both have been given in the question. A vector, given its magnitude and direction, can be derived by multiplying its mag. and dir. The direction, however, should be the unit vector in the given direction. Else, we will make a mistake by including the magnitude of 1+2j. The unit vector is derived by dividing the given vector by its magnitude. Thus,
the asnwer should be V= magnitude * unit vector in the direction of 1+2j.
which is the given answer
- 1 decade ago
Constant speed = 10 (5)^1/2
Direction vector = (i+2j)/(1+4)^1/2
= 1/(5)^1/2. (i+2j)
velocity = 10 (5)^1/2. 1/(5)^1/2. (i+2j)
= 10 (i+2j)
