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A bowling ball dropped from a height of 400feet will be s(t)=400-16t2feet from the ground after tseconds. Use a sequence of average velocities to estimate the instantaneous velocities described below:

When the bowling ball is first dropped, with h=0.5,h=0.25,andh=0.1

Short Answer

Expert verified

Ans: When h=0.5instantaneous velocity is: -8

When h=0.25instantaneous velocity is: -4

When h=0.1instantaneous velocity is:-1.6

Step by step solution

01

Step 1. Given information.

given,

A ball is dropped from a height of 400feet and its distance from the ground after tseconds is, s(t)=400-16t2

The objective is to estimate the instantaneous velocities for,

h=0.5,h=0.25,h=0.1
02

Step 2. When the ball has just dropped the value of c=0.

To find the instantaneous velocity for h=0.5follows the steps:

Now,

f(c)=f(0)=400

And

f(c+h)=f(0.5)=396

therefore the instantaneous velocity is:

f(c+h)-f(c)h=396-4000.5=-8

03

Step 3. To find the instantaneous velocity for h=0.25 follows the steps:

f(c)=f(0)=400

And,

f(c+h)=f(0.25)=399

therefore the instantaneous velocity is:

f(c+h)-f(c)h=399-4000.25=-4

f(c+h)=f(0.25)=399
04

Step 4. To find the instantaneous velocity for h=0.1 follows the steps:

f(c)=f(0)=400

And,

f(c+h)=f(0.1)=399.84

therefore the instantaneous velocity is:

f(c+h)-f(c)h=399.84-4000.1=-1.6

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