Answered: An alien on another planet throws a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

An alien on another planet throws a ball is thrown into the air. Its height (in feet) after t seconds is given by f(t)=51t−14t^2.

Find the average velocities, Round to 3 decimal places.

The average velocity between 1.4 and 2.4 seconds, between 3.9 and 4.4 seconds.

Find the instantaneous velocity at 1 second.

Expert Solution

Step 1

Given that, the function is $f (t) = 51 t - 14 t^{2}$ .

Obtain the average velocity between 1.4 and 2.4 seconds.

$\begin{array}{rcl} \frac{f (b) - f (a)}{b - a} & = & \frac{f (2.4) - f (1.4)}{2.4 - 1.4} \\ = & \frac{(51 (2.4) - 14 {(2.4)}^{2}) - (51 (1.4) - 14 {(1.4)}^{2})}{1} \\ = & - 2.2 \end{array}$

Therefore, the average velocity between 1.4 and 2.4 seconds is -2.2.

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