Question

You are falling down a chasm at 9.80 m/s2. It's a deep chasm, and you've got a calculator with you. If you are currently hurtling toward your doom at 23.016 m/s, how many seconds will it take you to reach terminal ivelocity of 195 km/h? Your answer must have the appropriate number of significant figures.

Answer 1

3.2 seconds

Explanation

Step 1

convert all measures in m.s.k system

so

$\begin{gathered} \text{aceleration}=a=9.8\text{ }\frac{m}{s^2} \\ \text{Inital sp}eed=v_0=23.016\text{ }\frac{m}{s} \\ \text{time}=\text{ t=unknown} \\ \text{ final sp}eed=v_f=195\text{ }\frac{\operatorname{km}}{h}\rightarrow it\text{ n}eeds\text{ to be converted, so} \\ 195\text{ }\frac{\operatorname{km}}{h}(\frac{1000\text{ m}}{1\text{ km}})(\frac{1\text{ hour}}{3600\text{ s}})=54.16\text{ }\frac{m}{s} \\ so,\text{ } \\ \text{ final sp}eed=v_f=54.16\text{ }\frac{m}{s} \end{gathered}$

Step 2

now, to figure out this we need to use the free fall formula:

$v_f=v_o+at$

hence, replace

$\begin{gathered} v_f=v_o+at \\ 54.16\frac{m}{s}=23.016\frac{m}{s}+9.8\frac{m}{s^2}\cdot t \\ 54.16=23.016+9.8t \end{gathered}$

Now, let's solve for t

$\begin{gathered} 54.16=23.016+9.8t \\ \text{subtract 23.016 in both sides} \\ 54.16-23.016=23.016+9.8t-23.016 \\ 31.15=9.8t \\ \text{divide both sides by 9.8} \\ \frac{31.15}{9.8}=\frac{9.8t}{9.8} \\ 3.178=t \\ \text{rounded} \\ t=3.2\text{ seconds} \end{gathered}$

therefore, the answer is

3.2 seconds

I hope this helps you