Please show mathematical and verbal work to answer all parts of the problem, add

Question

Please show mathematical and verbal work to answer all parts of the problem, additional discussion of the problem and how it is useful, and a graph of the function and its derivative.

Create and comment on the application in general and the graphs of the function and its derivative, too.

A feather dropped on the moon On the moon, a feather will fall to the ground at the same rate as a heavy stone. Suppose a feather is dropped from a height of 40 m above the surface of the moon. Then, its height s (in meters) above the ground after t seconds is s = 40-0.8 r. Determine the velocity and acceleration of the feather the moment it strikes the surface of the moon.

Explanation / Answer

First, we need to find t when s = 0 ( when it strikes the surface of the moon)

s=0 ;

40 - 0.8 t^2 = 0 ==> 0.8 t^2 = 40 ==> t^2 =50 t= sqrt (50) or t = - sqrt (50)

Since t >0, then t = sqrt(50)

Now, Velocity when t = 50 means

v(t) = s'(t) = -1.6t

when t = sqrt (50) , velocity = s'(sqrt(50)) = -1.6 * sqrt(50)

Acceleration = v'(t) = -1.6

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