Free fall

The free fall body has gone 10m in the last 0.5s. Find the body speed at the moment of impact.

Correct answer:

v =  22.5 m/s

Step-by-step explanation:

$$\begin{gathered} t=0.5\text{ s } \\ s=10\text{ m } \\ g=10{\text{m/s}}^2 \\ s={\displaystyle \frac{1}{2}}\cdot g\cdot t_1^2-{\displaystyle \frac{1}{2}}\cdot g\cdot (t_1-t{)}^2 \\ 2\cdot s\mathrm{/}g=t_1^2-(t_1-t{)}^2 \\ 2\cdot s\mathrm{/}g=t_1^2-t_1^2+2\cdot t\cdot t_1-t^2 \\ 2\cdot s\mathrm{/}g+t^2=2\cdot t\cdot t_1 \\ {t}_1={\displaystyle \frac{t^2+2\cdot s\mathrm{/}g}{2\cdot t}}={\displaystyle \frac{0.5^2+2\cdot 10\mathrm{/}10}{2\cdot 0.5}}={\displaystyle \frac{9}{4}}=2.25\text{ s } \\ v=g\cdot t_1=10\cdot 2.25={\displaystyle \frac{45}{2}}={\displaystyle \frac{45}{2}}\text{ m/s}=22.5\text{ m/s} \end{gathered}$$

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