Question

Picnickers see a lightning flash and hear the resulting thunder 9.80 s later. If the storm is traveling at a rate of 16.0 km/h, how long, in minutes, do the picnickers have before the storm arrives at their location? answer in:____min

Answer 1

13 minutes

Step-by-step explanation

Step 1

find the distance to thunder

a) let d represents the distance

let t represents the time,

the distance traveled by the ligth is given by:

`\begin{gathered} distance=\text{ speed of ligth*time} \\ replace \\ \\ d=(1.08*10^9\text{ }(km)/(h))t\rightarrow equation(1) \\ for\text{ d in km , and t is hours} \end{gathered}`

and

the distance traveled by the sound

i) convert the 9.8 seconds into hours

`9.8\text{ s}*\frac{1\text{ hour}}{3600\text{ s}}=0.00272222222\text{ hours}`

and

`speed\text{ of sound=1234.8 km/h}`

`\begin{gathered} distance2=\text{ speed of sound*\lparen t+0.00272222222\rparen} \\ d=1234.8(t+0.00272222222) \\ d=1234.8t+3.3614\Rightarrow equation(2) \end{gathered}`

use equation (1) and equatin (2) to solve for t

`\begin{gathered} distance1=\text{ distance 2} \\ replace \\ (1.08*10^9\text{ }(km)/(h))t=1234.8t+3.3614 \\ t(1.08*10^9-1234.8)=3.3614 \\ t=(3.3614)/((1.08*10^9-1234.8)) \\ \\ t=3.11*10^(-9) \end{gathered}`

now, replace in the equation (1) to find the distance

so,

the distance to the center of the sterom is 3.36 Km

Step 2

now, to know the time of the storm to arrive, we need to aply the formula

`\begin{gathered} time=(distance)/(speed) \\ so \\ time=\frac{3.36\text{ km}}{16\text{ km/h}}=0.21\text{ hours} \end{gathered}`

finally, to conver from hours to miinutes, multiply by 60

so

`\begin{gathered} 0.21\text{ hours}\Rightarrow0.21*60=12.605\text{ minutes} \\ rounded \\ 13\text{ minutes} \end{gathered}`

therefore, the answer is 13 minutes

I hope this helps you