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A student dropped a textbook from the top floor of his dorm and it fell according to the formula s(t) = −16t 2 + 8√t , where t is the time in seconds and s(t) is the distance in feet from the top of the building.What was the average speed of the fall? Use the fact that the pencil hit the ground in exactly 2.8 seconds. Round your answer to 2 decimal places.



Answer :

abidemiokin

Answer:

-29.61m/s

Step-by-step explanation:

Given the distance of fall of the student in term of the time t expressed by the equation s(t) = −16t² + 8√t, to get the average speed of fall of the pencil after 2.8 secs, we will need to differentiate the given function first since Velocity is the change in distance of a body with respect to time i.e

V = d(s(t))/dt

s(t) = −16t² + 8t^1/2

V = -32t+1/2(8)t^(1/2 - 1)

V = -32t+4t^-1/2

The average speed of the fall Using the fact that the pencil hit the ground in exactly 2.8 seconds, will be gotten by substituting t = 2.8 into the resulting equation.

V = -32t+4(2.8)^-1/2

V = -32t+4/√2.8

V = -32+4/1.6733

V = -32+2.391

v = -29.61m/s

Hence the average speed of the fall is -29.61m/s

The  average speed of the fall is -29.61m/s

Calculation of the average speed:

[tex]V = d(s(t))\div dt\\\\s(t) = −16t^2 + 8t^{1/2}\\\\V = -32t+1/2(8)t^{(1/2 - 1)}\\\\V = -32t+4t^{-1/2}[/tex]

Now here t = 2.8 seconds

So,

[tex]V = d(s(t))\div dt\\\\s(t) = −16t^2 + 8t^{1/2}\\\\V = -32t+1/2(8)t^{(1/2 - 1)}\\\\V = -32t+4t^-1/2[/tex]

V = -32+2.391

v = -29.61m/s

Learn more about the speed here: https://brainly.com/question/13373304