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kifflom
3 months ago
13

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 i

s 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.
Mathematics
1 answer:
Zina [12.3K]3 months ago
3 0

Answer:

-29.61m/s

Step-by-step explanation:

To find the average speed of the pencil after dropping it for 2.8 seconds, we start with the fall distance equation for the student, s(t) = −16t² + 8√t. First, we differentiate this function since velocity is the rate of change of distance with respect to time, expressed as

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

To find the average speed, we substitute t = 2.8 into the derived equation since the pencil reaches the ground precisely after 2.8 seconds.

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

V = -32 + 4/√2.8

V = -32 + 4/1.6733

V = -32 + 2.391

v = -29.61m/s

Thus, the average speed at which it fell is -29.61m/s

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