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Answer :
Sure! Let's solve this problem step-by-step.
Question:
A blimp is descending at a constant speed of 5.2 meters per second from a height of 1,500 meters above the ground. Which equation models the height, [tex]\( h \)[/tex], of the blimp in meters after [tex]\( t \)[/tex] seconds?
Options:
A. [tex]\( h = 5.21 \)[/tex]
B. [tex]\( h = 1500 + 5.2t \)[/tex]
C. [tex]\( h = 1500 - 5.2t \)[/tex]
D. [tex]\( \frac{15010}{52t} \)[/tex]
Solution:
1. Identify the initial height and descent rate:
- Initial height of the blimp: [tex]\( 1500 \)[/tex] meters
- Constant descent speed: [tex]\( 5.2 \)[/tex] meters per second
2. Understand the problem:
- The blimp is descending, which means its height decreases over time.
- We need an equation that starts from the initial height and subtracts the total distance descended over time.
3. Formulate the equation:
- The blimp descends [tex]\( 5.2 \)[/tex] meters each second.
- After [tex]\( t \)[/tex] seconds, the total descent is [tex]\( 5.2t \)[/tex] meters.
- Therefore, the height [tex]\( h \)[/tex] after [tex]\( t \)[/tex] seconds can be calculated by subtracting the total descent from the initial height:
[tex]\[
h = 1500 - 5.2t
\][/tex]
4. Compare with the given options:
- Option A: [tex]\( h = 5.21 \)[/tex] (doesn't make sense as it doesn't involve time [tex]\( t \)[/tex])
- Option B: [tex]\( h = 1500 + 5.2t \)[/tex] (incorrect because it suggests the height increases with time)
- Option C: [tex]\( h = 1500 - 5.2t \)[/tex] (correct, matches our derived equation)
- Option D: [tex]\( \frac{15010}{52t} \)[/tex] (incorrect, this form does not match the linear relationship we derived)
Therefore, the correct model for the height of the blimp after [tex]\( t \)[/tex] seconds is:
[tex]\[ \boxed{h = 1500 - 5.2t} \][/tex]
Thus, the correct answer is option C.
Question:
A blimp is descending at a constant speed of 5.2 meters per second from a height of 1,500 meters above the ground. Which equation models the height, [tex]\( h \)[/tex], of the blimp in meters after [tex]\( t \)[/tex] seconds?
Options:
A. [tex]\( h = 5.21 \)[/tex]
B. [tex]\( h = 1500 + 5.2t \)[/tex]
C. [tex]\( h = 1500 - 5.2t \)[/tex]
D. [tex]\( \frac{15010}{52t} \)[/tex]
Solution:
1. Identify the initial height and descent rate:
- Initial height of the blimp: [tex]\( 1500 \)[/tex] meters
- Constant descent speed: [tex]\( 5.2 \)[/tex] meters per second
2. Understand the problem:
- The blimp is descending, which means its height decreases over time.
- We need an equation that starts from the initial height and subtracts the total distance descended over time.
3. Formulate the equation:
- The blimp descends [tex]\( 5.2 \)[/tex] meters each second.
- After [tex]\( t \)[/tex] seconds, the total descent is [tex]\( 5.2t \)[/tex] meters.
- Therefore, the height [tex]\( h \)[/tex] after [tex]\( t \)[/tex] seconds can be calculated by subtracting the total descent from the initial height:
[tex]\[
h = 1500 - 5.2t
\][/tex]
4. Compare with the given options:
- Option A: [tex]\( h = 5.21 \)[/tex] (doesn't make sense as it doesn't involve time [tex]\( t \)[/tex])
- Option B: [tex]\( h = 1500 + 5.2t \)[/tex] (incorrect because it suggests the height increases with time)
- Option C: [tex]\( h = 1500 - 5.2t \)[/tex] (correct, matches our derived equation)
- Option D: [tex]\( \frac{15010}{52t} \)[/tex] (incorrect, this form does not match the linear relationship we derived)
Therefore, the correct model for the height of the blimp after [tex]\( t \)[/tex] seconds is:
[tex]\[ \boxed{h = 1500 - 5.2t} \][/tex]
Thus, the correct answer is option C.
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