Let's tackle each part of the question step-by-step.
### Part 1: Convert 212 ft/hr to cm/s and m/s
#### a. Convert 212 ft/hr to cm/s
Given:
- 1 foot (ft) = 30.48 centimeters (cm)
- 1 hour (hr) = 3600 seconds (s)
Steps:
1. Convert feet to centimeters:
[tex]\( 212 \, \text{ft} = 212 \times 30.48 \, \text{cm} \)[/tex]
2. Convert the hourly rate to a per second rate:
[tex]\( \frac{212 \times 30.48 \, \text{cm}}{3600 \, \text{s}} \)[/tex]
After performing the calculations, you have:
- [tex]\( 212 \, \text{ft/hr} = 1.7949333333333335 \, \text{cm/s} \)[/tex]
#### b. Convert 212 ft/hr to m/s
Given:
- 1 centimeter (cm) = 0.01 meters (m)
Steps:
1. Use the conversion from cm/s obtained in part a:
[tex]\( 1.7949333333333335 \, \text{cm/s} \)[/tex]
2. Convert centimeters to meters:
[tex]\( 1.7949333333333335 \, \text{cm/s} \times 0.01 = 0.017949333333333335 \, \text{m/s} \)[/tex]
After performing the conversions, you have:
- [tex]\( 212 \, \text{ft/hr} = 0.017949333333333335 \, \text{m/s} \)[/tex]
### Part 2: Convert the lengths to inches and sum them
Given:
- Length in meters (m) = 2.4 m
- Length in feet (ft) = 32 ft
- Length in centimeters (cm) = 35 cm
Conversions needed:
- 1 meter (m) = 39.3701 inches (in)
- 1 foot (ft) = 12 inches (in)
- 1 centimeter (cm) = 0.393701 inches (in)
Steps:
1. Convert meters to inches:
[tex]\( 2.4 \, \text{m} \times 39.3701 \, \text{in/m} = 94.48824 \, \text{in} \)[/tex]
2. Convert feet to inches:
[tex]\( 32 \, \text{ft} \times 12 \, \text{in/ft} = 384 \, \text{in} \)[/tex]
3. Convert centimeters to inches:
[tex]\( 35 \, \text{cm} \times 0.393701 \, \text{in/cm} = 13.779535 \, \text{in} \)[/tex]
Now sum these lengths:
- Total length in inches = [tex]\( 94.48824 + 384 + 13.779535 = 492.267775 \, \text{in} \)[/tex]
Thus, the total length is [tex]\( 492.26777500000003 \)[/tex] inches.
### Summary:
1. [tex]\( 212 \, \text{ft/hr} \)[/tex] converts to:
- [tex]\( 1.7949333333333335 \, \text{cm/s} \)[/tex]
- [tex]\( 0.017949333333333335 \, \text{m/s} \)[/tex]
2. The total length of 2.4 m + 32 ft + 35 cm is [tex]\( 492.26777500000003 \)[/tex] inches.
