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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:

After t=1 seconds, with h=0.5,h=0.25,h=-0.5andh=-0.2

Short Answer

Expert verified

Ans: When h=0.5instantaneous velocity is: -40

When h=0.25instantaneous velocity is: -36

When h=-0.5instantaneous velocity is: -24

When h=-0.2instantaneous velocity is:-28.8

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)=40016t2

The objective is to estimate the instantaneous velocities for,

h=0.5,h=0.25,h=-0.5andh=-0.2
02

Step 2. When the ball has just dropped the value of t=1.

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

Now,

f(t)=f(1)=384

And

f(t+h)=f(1.5)=364

Therefore the instantaneous velocity is:

f(t+h)f(t)h=3643840.5=200.5=40

03

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

f(t)=f(1)=384

And

f(t+h)=f(1.25)=375

Therefore the instantaneous velocity is:

f(t+h)f(t)h=3753840.25=90.25=36

04

Step 4. To find the instantaneous velocity for h=-0.5 follows the steps:

And

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

Therefore the instantaneous velocity is:

f(t+h)f(t)h=3963840.5=120.5=24

05

Step 5. To find the instantaneous velocity for h=-0.2 follows the steps:

f(t)=f(1)=384

And

f(t+h)=f(0.8)=389.76 f(t+h)=f(0.8)=389.76

Therefore the instantaneous velocity is:

f(t+h)f(t)h=389.763840.2=5.760.2=28.8

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