   Chapter 10.5, Problem 86E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Velocity If a stone is thrown down at 120 ft/s from a height of 1,000 feet, its height after t seconds is given by s = 1 , 000 − 120 − 16 t 2 . a. Find its average velocity over the period [ 1 , 3 ] .b. Estimate its instantaneous velocity at time t = 3 . [HINT: See Example 3.]

(a)

To determine

To calculate: The average velocity of the stone which is dropped from the height of 1000m with velocity 120ft/sec between the time interval [1,3] provided that the height after t seconds is expressed as s=1000120t16t2.

Explanation

Given information:

The stone is dropped at the height of 1000m with velocity 120ft/sec, the height after t seconds is expressed as s=1000120t16t2.

Formula used:

The average rate of change of function f(x) is:

Average rate of change=ΔfΔt

Calculation:

Consider the function for height after t seconds, s=1000120t16t2.

Evaluate the change in height from t=1 to t=3

Δs=s(3)s(1)

Evaluate the value of s(1).

s=1000120t16t2s(1)=1000120(1)16(1)2=100012016=864

Evaluate the value of s(3)

(b)

To determine

To calculate: The instantaneous velocity of the stone which is dropped at the height of 1000m with velocity 120ft/sec at t=3sec provided that the height after t seconds is expressed as s=1000120t16t2.

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