Answer
$25$ sec.
$694.4$ m.
Work Step by Step
Step 1. Given the equation $D=\frac{10}{9}t^2$, we have the speed $v(t)=\frac{dD}{dt}=\frac{20}{9}t$ m/s
Step 2. At a speed of $v=200km/h=200000/3600=\frac{500}{9}$ m/s, we have $\frac{20}{9}t=\frac{500}{9}$, which gives $t=25$ sec. Thus it will take $25$ seconds for the airplane to become airborne.
Stpe 3. At $t=25$, we have $D=\frac{10}{9}(25)^2=\frac{6250}{9}\approx694.4$ m.
