Question

c. the speed of an object is 1.0793 x 10^9 km/h, convert it to mi/s, and to ft/min.

Explanation:

Step1: Convert km/h to mi/s

• First, convert kilometers to miles: \(1\) km \(=\frac{1}{1.60934}\) mi.
• Then, convert hours to seconds: \(1\) h \( = 3600\) s.
• So, \(1.0793\times10^{9}\) km/h\(=1.0793\times 10^{9}\times\frac{1}{1.60934}\times\frac{1}{3600}\) mi/s.
• Calculate \(\frac{1.0793\times 10^{9}}{1.60934\times3600}\)

\(1.60934\times3600 = 5793.624\)
\(\frac{1.0793\times 10^{9}}{5793.624}\approx1.863\times 10^{5}\) mi/s.

Step2: Convert km/h to ft/min

• Convert kilometers to feet: \(1\) km \( = 3280.84\) ft.
• Convert hours to minutes: \(1\) h \(= 60\) min.
• So, \(1.0793\times10^{9}\) km/h\(=1.0793\times 10^{9}\times3280.84\times\frac{1}{60}\) ft/min.
• Calculate \(1.0793\times 10^{9}\times\frac{3280.84}{60}\)

\(\frac{3280.84}{60}\approx54.6807\)
\(1.0793\times 10^{9}\times54.6807\approx5.90\times 10^{10}\) ft/min.

Answer:

The speed is approximately \(1.863\times 10^{5}\) mi/s and \(5.90\times 10^{10}\) ft/min.