Respuesta :
3.2 s
Explanation
Step 1
Let
[tex]\begin{gathered} \text{aceleration}=a=9.8\text{ }\frac{m}{s^2} \\ \text{ Initial sp}eed=v_0=23.016\text{ }\frac{m}{s} \\ \text{time}=\text{ t=unknown} \\ \text{ final sp}eed=195\text{ }\frac{\operatorname{km}}{\text{h}} \end{gathered}[/tex]
to solve this we need to use the free fall formula:
[tex]v_f=v_0+at[/tex]in order to use that formula, we need to have the same measure unit on each data, we will use meters, seconds, so we need to convert hte final velocity from KM/h into m/s
so
[tex]\begin{gathered} 195\text{ }\frac{\text{km}}{h} \\ Multiply\text{ by equivalent fractions} \\ 195\frac{\text{km}}{h}\cdot(\frac{1\text{ hour}}{3600\text{ sec}})(\frac{1000\text{ m}}{1\text{ km}})=54.16\text{ m/s} \end{gathered}[/tex]now, we can replace the data into the formula:
Step 2
replace
[tex]\begin{gathered} v_f=v_0+at \\ 54.16\text{ }\frac{m}{s}=23.016\text{ }\frac{m}{s}+(9.8\frac{m}{s^2}\cdot t) \\ 54.16=23.016+9.8t \\ \text{solve for t} \\ \text{subtract 23.016 in both sides} \\ 54.16-23.016=23.016+9.8t-23.016 \\ 31.15=9.8t \\ \text{divide both sides by 9.8} \\ \frac{31.15}{9.8}=\frac{9.8t}{9.8} \\ 3.17\text{ s=t} \\ \text{rounded} \\ t=3.2\text{ seconds} \end{gathered}[/tex]therefore, the answer is
3.2 seconds
