A object is thrown from the top of a connung und ralls to the ground below. Its path is approximated by therelation h(t) = -5² + 10t + 120, where h is the height above the ground in metres after t seconds. Determine theaverage velocity of the object during its last 3 seconds in the air.

Answered: A object is thrown from the top of 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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A object is thrown from the top of a connung und ralls to the ground below. Its path is approximated by the
relation h(t) = -5² + 10t + 120, where h is the height above the ground in metres after t seconds. Determine the
average velocity of the object during its last 3 seconds in the air.

Expert Solution

Step 1

The given position function is $h (t) = - 5 t^{2} + 10 t + 120$ .

The objective is to calculate the average velocity of the object during last $3$ seconds in the air.

Calculate the time when the particle hit the ground.

Equate the expression of $h (t)$ with $0$ and simplify to calculate the value of $t$ .

$\begin{array}{rcl} h (t) & = & 0 \\ - 5 t^{2} + 10 t + 120 & = & 0 \\ t^{2} - 2 t - 24 & = & 0 \\ t^{2} - 6 t + 4 t - 24 & = & 0 \\ t (t - 6) + 4 (t - 6) & = & 0 \\ (t - 6) (t + 4) & = & 0 \\ t & = & - 4, 6 \end{array}$

The time is always positive. Therefore, the value of $t = 6$ .

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A object is thrown from the top of a coming and rails to the ground below. Its path is approximated by the relation h(t) = -5² + 10t + 120, where h is the height above the ground in metres after t seconds. Determine the average velocity of the object during its last 3 seconds in the air.