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 velocity of 195 km/h? Your answer must have the appropriate number of significant figures.

Answer 1

3.2 s

Step-by-step explanation

Step 1

Let

to solve this we need to use the free fall formula:

`v_f=v_0+at`

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

`\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}`

now, we can replace the data into the formula:

Step 2

replace

`\begin{gathered} v_f=v_0+at \\ 54.16\text{ }(m)/(s)=23.016\text{ }(m)/(s)+(9.8(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} \\ (31.15)/(9.8)=(9.8t)/(9.8) \\ 3.17\text{ s=t} \\ \text{rounded} \\ t=3.2\text{ seconds} \end{gathered}`

therefore, the answer is

3.2 seconds