- #1

Northbysouth

- 249

- 2

## Homework Statement

A certain lake is proposed as a landing area for large jet aircraft. The touchdown speed of 110 mi/hr upon contact with the water is to be reduced to 24 mi/hr in a distance of 1370 ft. If the deceleration is proportional to the square of the velocity of the aircraft through the water, a = -Kv2, find the value of the design parameter K, which would be a measure of the size and shape of the landing gear vanes that plow through the water. Also find the time t elapsed during the specified interval.

## Homework Equations

x = x

_{0}+ v

_{0x}t + 1/2at

^{2}

v = v

_{0x}+ at

## The Attempt at a Solution

v = v

_{0x}+ at

24 mi/hr = 110 mi/hr - (kv

^{2})t

24 mi/hr = 110 mi/hr -576kt

576kt = 86 mi/hr

t = 86/576k

Taking this I plugged it into

x = x

_{0}+ v

_{0x}t + 1/2at

^{2}

1370ft = 0 + (110mi/hr)t + 1/2(-kv

^{2})t

^{2}

Plugged in v = 24 mi/hr

1370ft = (110 mi/hr)5 - 288 kt

^{2}

1370 ft = (110 mi/hr)(86/576k) - 288(86/576)

k = 0.01162

t = 12/845

I realize that I entered my value for k into the system incorrectly, but I used that value to calculate t, which was incorrect. With that said, I'm not sure what to do. Suggestions are welcome and appreciated. THanks