Final answer:
The jet's velocity adjusts to the crosswind, taking into account the initial direction and speed of the jet and the direction and speed of the wind. The true velocity of the jet in component form, considering west as 'i' and south as 'j', is: w=260i - 125j (mi/h).
Step-by-step explanation:
The given information allows us to calculate the true velocity of the jet by using vector addition, where we will add the jet's velocity and the wind's velocity, both considered as vectors. The jet's direction, S60°W, means it heads 60° west from due south. In vector terms, it has components towards west and towards south.
We have:
- Jet's speed towards the south = 300cos(60°) = 150 mi/h
- Jet's speed towards the west = 300sin(60°) = 260 mi/h
The 25 mi/h crosswind flows due north, which, being opposite to the jet's southern component of velocity, will subtract from it.
Therefore, the true velocity of the jet when taking the crosswind into account has:
- a southern component = 150 mi/h - 25 mi/h = 125 mi/h , and
- a western component = 260 mi/h (unchanged as the wind is flowing due north).
In component form, the true velocity w of the jet is: w = 260i - 125j (mi/h), taking west as positive direction for 'i' component and south as negative direction for 'j' component.
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