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Part $1$

On a certain$$ planet, you bail out of a helicopter and immediately open your parachute. For the gravity and atmosphere on this$$ planet, your downward velocity satisfies the following initial value problem$($with t in seconds and v in$$ ft$/$s$).$

StartFraction dv Over dt EndFractionequals$21$minus$1\mathrm{.}4$v$,$

v left parenthesis $0$ right parenthesisequals$0$

Use the improved Euler method with a programmable calculator or computer to approximate the solution for

$0$less than over equaltless than over equal$2,$

first with step size

hequals$0\mathrm{.}01$

and then with

hequals$0\mathrm{.}005.$

What percentage of the limiting velocity

$15$

$$ft$/$s has been attained after $1$ second? After $2$ seconds?

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Part $1$

Find the approximate velocity after $1$ second.

$($Round to three decimal places as$$ needed.$)$

With

hequals$0\mathrm{.}01,$

the approximate velocity after $1$ second is

enter your response here

$$ft$/$sec$.$