Question

Col. Joe Kittinger of the United States Air Force crossed the Atlantic Ocean in nearly 86 hours. The distance he traveled was 57000 m. Suppose Col. Kittinger is moving with a constant acceleration during most of his flight and that his final speed is 10.0 percent greater than his initial speed. Find the initial speed based on this data.

Answer 1

Initial speed Vo=631.229 mi/h

Step-by-step explanation:

For this problem, I used miles instead of meters, because that seems more accurate. Since the final speed is 10% (0.1) higher than initial, then mathematically it means

`V_(f)=V_(o)+0.1*V_(o)=1.1*V_(o)`

First, find the acceleration, with this formula

`V^(2) _(f)-V^(2)_(o)=2*a*dist`

Which results in

`a=((1.1*V _(o))^(2)-V^(2)_(o))/(2*57000) =0.000002*V_(o)^(2)`

Now substitute in this equation:

`V _(f)-V_(o)=a*t\\ (1.1-1)*V_(o)=0.000002*V_(o)^(2)*86`

This became in a quadratic equation. Dividing both sides by initial speed and solving and, since we used time in Hours and for distance miles, then the speed should have units of miles per hour:

`0.1*V_(o)=0.000158*V_(o)x^(2) \\ V_(o)=631.229mi/h`