Question

Answer 1

\(h=\dfrac{1}{2}t^2+\dfrac{1}{2}t\Rightarrow8h=4t^2+4t\)

\(\Rightarrow8h+1=4t^2+4t+1=\left(2t+1\right)^2\)

\(\Rightarrow2t+1=\sqrt[]{8h+1}\)

\(\Rightarrow t=\dfrac{1}{2}\sqrt[]{8h+1}-\dfrac{1}{2}\)

Ý nghĩa: để đạt độ cao h thì khí cầu cần mất thời gian \(t=\dfrac{1}{2}\sqrt[]{8h+1}-\dfrac{1}{2}\)

a. 

\(h=120\Rightarrow t=\dfrac{1}{2}\sqrt[]{8.120+1}-\dfrac{1}{2}=15\left(s\right)\)

\(h=210\Rightarrow t=\dfrac{1}{2}\sqrt[]{8.210+1}-\dfrac{1}{2}=20\left(s\right)\)