Question

The velocity, in feet per second, of a rocket $t$ sec into vertical flight is given by $$v(t)=-3 t^{2}+192 t$$ Find an expression $h(t)$ that gives the rocket's altitude, in feet, $t$ sec after liftoff. What is the altitude of the rocket 30 sec after liftoff?

Name: Problem 79, Chapter 6: Applied Calculus for the MLSS A Brief Approach
Uploaded: 2021-08-01T00:02:35-08:00
Duration: 1 min 13 s
Channel: Lucas Finney
Description: The velocity, in feet per second, of a rocket t sec into vertical flight is given by v(t)=-3 t^2+192 t Find an expression h(t) that gives the rocket's altitude, in feet, t sec after liftoff. What is the altitude of the rocket 30 sec after liftoff?

   The velocity, in feet per second, of a rocket $t$ sec into vertical flight is given by
$$v(t)=-3 t^{2}+192 t$$
Find an expression $h(t)$ that gives the rocket's altitude, in feet, $t$ sec after liftoff. What is the altitude of the rocket 30 sec after liftoff?

Applied Calculus for the MLSS A Brief Approach

Soo T. Tan 10th Edition

Chapter 6, Problem 79

Instant Answer

Solved by Expert Lucas Finney

08/01/2021

Step 1

To find the altitude of the rocket, we need to find the antiderivative of the velocity function, which will give us the position function $h(t)$. Show more…

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The velocity, in feet per second, of a rocket $t$ sec into vertical flight is given by $$v(t)=-3 t^{2}+192 t$$ Find an expression $h(t)$ that gives the rocket's altitude, in feet, $t$ sec after liftoff. What is the altitude of the rocket 30 sec after liftoff?

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Key Concepts

Antiderivative

An antiderivative is a function whose derivative is the original function. By finding the antiderivative of the velocity function, we obtain the altitude function, which can then be evaluated at specific points in time.

Integration

Integration is the process of finding the antiderivative of a function. In this context, it is used to determine the position function from the given velocity function by integrating with respect to time.

Kinematics and Initial Conditions

In kinematics, the displacement or altitude is obtained by integrating the velocity function. The integration process introduces an arbitrary constant, which is determined using the initial condition, such as the initial altitude at liftoff.

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