Giving a vertical velocity v(t)= 4t +3 (ft/sec) for a helicopter t seconds after took off. The helicopter was observed 16 feet above the sea level, after taking off for 2 seconds. Find a formula that gives height of the helicopter at any time t? (Hint: v(t)=h'(t) where h(t) is the height of the helicopter at any time t.)

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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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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**Velocity and Height of a Helicopter**

Given a vertical velocity \( v(t) = 4t + 3 \) (ft/sec) for a helicopter \( t \) seconds after takeoff.

The helicopter was observed 16 feet above sea level after taking off for 2 seconds.

Find a formula that gives the height of the helicopter at any time \( t \). 

*(Hint: \( v(t) = h'(t) \) where \( h(t) \) is the height of the helicopter at any time \( t \).)*

**Explanation of Hint:**  
The velocity function \( v(t) \) represents the derivative of the height function \( h(t) \), which describes how the height of the helicopter changes over time. To find the height function \( h(t) \), you need to integrate the velocity function \( v(t) \). The condition that the helicopter was 16 feet above sea level at \( t = 2 \) seconds will help determine the constant of integration.
Transcribed Image Text:**Velocity and Height of a Helicopter** Given a vertical velocity \( v(t) = 4t + 3 \) (ft/sec) for a helicopter \( t \) seconds after takeoff. The helicopter was observed 16 feet above sea level after taking off for 2 seconds. Find a formula that gives the height of the helicopter at any time \( t \). *(Hint: \( v(t) = h'(t) \) where \( h(t) \) is the height of the helicopter at any time \( t \).)* **Explanation of Hint:** The velocity function \( v(t) \) represents the derivative of the height function \( h(t) \), which describes how the height of the helicopter changes over time. To find the height function \( h(t) \), you need to integrate the velocity function \( v(t) \). The condition that the helicopter was 16 feet above sea level at \( t = 2 \) seconds will help determine the constant of integration.
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