The problem and solution involving the ballistic missile question is in the attached picture.
The Attempt at a Solution
Why does the first expression have (24)(6) in the denominator, when the second expression has (24)(6)(2) ?
My thought process:
If the missile could teleport to latitude 45 right after being launched from latitude 30, and have the velocity of latitude 30, then I can see why the first expression (without the 2) is valid.
But instead, the missile needs to gradually work its way to having that large of a relative velocity as it moves north. So it goes from 0 relative velocity to the full relative velocity and so dividing by 2 will get the average relative velocity.
Then i had doubts that the relationship between relative velocity and time was linear. I worked out some math and it seemed like a trigonometric relationship with velocity being proportional to cosine(arclength).
Am i confusing myself?
I would appreciate it if someone could clarify this for me.
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