Question

a parachutists rate during a free fall reaches 162 kilometers per hour. what is this rate in meters per second? at this rate, how many meters will the parachutist fall during 15 seconds of free fall? do not round your answers. rate: \\(\frac{m}{s}\\) distance fallen in 15 seconds: \\(m\\)

Explanation:

Step1: Convert km/h to m/s

We know that 1 kilometer = 1000 meters and 1 hour = 3600 seconds. So to convert 162 km/h to m/s, we use the conversion factors:
\[
162\ \frac{\text{km}}{\text{h}} = 162\times\frac{1000\ \text{m}}{3600\ \text{s}}
\]
Simplify the fraction \(\frac{1000}{3600}=\frac{5}{18}\), then:
\[
162\times\frac{5}{18}=\frac{162\times5}{18} = \frac{810}{18}=45\ \frac{\text{m}}{\text{s}}
\]

Step2: Calculate distance fallen in 15 seconds

The formula for distance \(d\) when speed \(v\) and time \(t\) are known is \(d = v\times t\). Here, \(v = 45\ \frac{\text{m}}{\text{s}}\) and \(t = 15\ \text{s}\), so:
\[
d=45\times15 = 675\ \text{m}
\]

Answer:

Rate: \(45\ \frac{\text{m}}{\text{s}}\)
Distance fallen in 15 seconds: \(675\ \text{m}\)