### Cliff Diver Plunge Problem A cliff diver plunges from a height of 36 ft above the water surface. The distance the diver falls in \( t \) seconds is given by the function \( d(t) = 16t^2 \) ft. #### Question 1: Time to Hit the Water Which equation can be solved for \( t \) to find the time (in seconds) when the diver hits the water? - \( 16t^2 - 36 = 36 \) - \( 16t^2 + 36 = -36 \) - \( 16t^2 = 0 \) - \( 16t^2 = 36 \) - \( 16t^2 + 36 = 0 \) After how many seconds will the diver hit the water? \[ \_\_\_\_\_\_ \text{s} \] #### Question 2: Velocity of the Diver at Impact Given that the velocity of the diver at time \( t = a \) is given by \[ \lim_{h \to 0} \frac{d(a + h) - d(a)}{h}, \] what value of \( a \) (in seconds) should be used to calculate the velocity of the diver when they hit the water? \[ a = \_\_\_\_\_\_ \text{s} \] #### Question 3: Distance Fallen by the Diver Determine the value of \( d(a) \) (in ft) when the diver hits the water. \[ d(a) = \_\_\_\_\_\_ \text{ft} \] #### Question 4: Impact Velocity of the Diver With what velocity (in ft/s) does the diver hit the water? \[ \_\_\_\_\_\_ \text{ft/s} \] --- The image contains a step-by-step problem regarding a cliff diver jumping into the water, illustrating questions that involve solving for time, velocity at impact, and the application of derivatives to determine these values.
### Cliff Diver Plunge Problem A cliff diver plunges from a height of 36 ft above the water surface. The distance the diver falls in \( t \) seconds is given by the function \( d(t) = 16t^2 \) ft. #### Question 1: Time to Hit the Water Which equation can be solved for \( t \) to find the time (in seconds) when the diver hits the water? - \( 16t^2 - 36 = 36 \) - \( 16t^2 + 36 = -36 \) - \( 16t^2 = 0 \) - \( 16t^2 = 36 \) - \( 16t^2 + 36 = 0 \) After how many seconds will the diver hit the water? \[ \_\_\_\_\_\_ \text{s} \] #### Question 2: Velocity of the Diver at Impact Given that the velocity of the diver at time \( t = a \) is given by \[ \lim_{h \to 0} \frac{d(a + h) - d(a)}{h}, \] what value of \( a \) (in seconds) should be used to calculate the velocity of the diver when they hit the water? \[ a = \_\_\_\_\_\_ \text{s} \] #### Question 3: Distance Fallen by the Diver Determine the value of \( d(a) \) (in ft) when the diver hits the water. \[ d(a) = \_\_\_\_\_\_ \text{ft} \] #### Question 4: Impact Velocity of the Diver With what velocity (in ft/s) does the diver hit the water? \[ \_\_\_\_\_\_ \text{ft/s} \] --- The image contains a step-by-step problem regarding a cliff diver jumping into the water, illustrating questions that involve solving for time, velocity at impact, and the application of derivatives to determine these values.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Cliff Diver Plunge Problem
A cliff diver plunges from a height of 36 ft above the water surface. The distance the diver falls in \( t \) seconds is given by the function \( d(t) = 16t^2 \) ft.
#### Question 1: Time to Hit the Water
Which equation can be solved for \( t \) to find the time (in seconds) when the diver hits the water?
- \( 16t^2 - 36 = 36 \)
- \( 16t^2 + 36 = -36 \)
- \( 16t^2 = 0 \)
- \( 16t^2 = 36 \)
- \( 16t^2 + 36 = 0 \)
After how many seconds will the diver hit the water?
\[ \_\_\_\_\_\_ \text{s} \]
#### Question 2: Velocity of the Diver at Impact
Given that the velocity of the diver at time \( t = a \) is given by
\[ \lim_{h \to 0} \frac{d(a + h) - d(a)}{h}, \]
what value of \( a \) (in seconds) should be used to calculate the velocity of the diver when they hit the water?
\[ a = \_\_\_\_\_\_ \text{s} \]
#### Question 3: Distance Fallen by the Diver
Determine the value of \( d(a) \) (in ft) when the diver hits the water.
\[ d(a) = \_\_\_\_\_\_ \text{ft} \]
#### Question 4: Impact Velocity of the Diver
With what velocity (in ft/s) does the diver hit the water?
\[ \_\_\_\_\_\_ \text{ft/s} \]
---
The image contains a step-by-step problem regarding a cliff diver jumping into the water, illustrating questions that involve solving for time, velocity at impact, and the application of derivatives to determine these values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4e135d5c-f867-4afd-9f0d-b505f4f19664%2Fbb9f51a9-9617-40ee-855e-7c4469352c70%2Fb3xl1uf_processed.png&w=3840&q=75)
Transcribed Image Text:### Cliff Diver Plunge Problem
A cliff diver plunges from a height of 36 ft above the water surface. The distance the diver falls in \( t \) seconds is given by the function \( d(t) = 16t^2 \) ft.
#### Question 1: Time to Hit the Water
Which equation can be solved for \( t \) to find the time (in seconds) when the diver hits the water?
- \( 16t^2 - 36 = 36 \)
- \( 16t^2 + 36 = -36 \)
- \( 16t^2 = 0 \)
- \( 16t^2 = 36 \)
- \( 16t^2 + 36 = 0 \)
After how many seconds will the diver hit the water?
\[ \_\_\_\_\_\_ \text{s} \]
#### Question 2: Velocity of the Diver at Impact
Given that the velocity of the diver at time \( t = a \) is given by
\[ \lim_{h \to 0} \frac{d(a + h) - d(a)}{h}, \]
what value of \( a \) (in seconds) should be used to calculate the velocity of the diver when they hit the water?
\[ a = \_\_\_\_\_\_ \text{s} \]
#### Question 3: Distance Fallen by the Diver
Determine the value of \( d(a) \) (in ft) when the diver hits the water.
\[ d(a) = \_\_\_\_\_\_ \text{ft} \]
#### Question 4: Impact Velocity of the Diver
With what velocity (in ft/s) does the diver hit the water?
\[ \_\_\_\_\_\_ \text{ft/s} \]
---
The image contains a step-by-step problem regarding a cliff diver jumping into the water, illustrating questions that involve solving for time, velocity at impact, and the application of derivatives to determine these values.
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