A ball is thrown into the air by a baby alien on a planet in the system of Alph

Question

A ball is thrown into the air by a baby alien on a planet in the system of Alph Centauri with a velocity of 44 ft/s. Its height in feet after t seconds is given by y = 44t-21t2 Find the average velocity for the time period beginning when t2 and lasting 01 s: Previewv Hint: This first interval of time is [2, 2 .01] [2, 2.01]. 005 s 002 s: Preview Preview Preview 001 s NOTE: For the above answers, use the exact coordinates for the points. You car your final result to 4 decimal places Estimate the instanteneous velocity when t=2. Preview Points possible: 12 This is attempt I of 2. Submit

Explanation / Answer

Solution:

y = 44t - 21t^2

a)
average velocity begining at 2 and lasting for 0.5 sec
(average velocity between 2 and 2.5)=

y(2) - y(2.5)/0.5 =

44(2) - 21(2)^2 - [44(2.5) - 21(2.5)^2]/0.5 =

(88 - 84)-[110 - 105]/0.5 =
4-5/0.5 =
1/0.5 = 2 ft/s

b)

average vel between t =2 and lasting for 0.1 sec

y(2) - y(2.1)/0.1 =

44(2) - 21(2)^2 - [44(2.1) - 21(2.1)^2]/0.1 =

(88 - 84) -[92.4 - 88.2]/0.1 =

4 - 4.2/0.1 =

2 ft/s

c) instantaneous v at t = 2 = y'(2)

y' = 44 - 42t

y'(2) = 44 - 42(2) =

44 - 84 =

-40 ft/s

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