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  3. 2 suppose an object of mass 15 kg is dropped...

Question: 2 suppose an object of mass 15 kg is dropped...

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2. Suppose an object of mass 15 kg is dropped from a height near the surface of the Earth, so the acceleration due to gravity is -9.8, and assume the drag due to air resistance is proportional to the square of objects velocity, with drag coefficient γ = 0.47. Assume the objects position is measured in meters above the ground, so velocity and acceleration are both negative. (a) Write down, but do not solve, a differential equation whose solution would give the objects current velocity t seconds after being dropped. (Hint: Think carefully about the fact that down is negative and youre squaring the velocity.) (b) Plot the slope field for the differential equation in part (a). You can plot this on a computer (e.g., using Sage) and either sketch the slope field by hand on paper or print out the slope field you plotted on the computer. (c) Based on the slope field from part (b), estimate the objects terminal velocity (You may want to play with the bounds for the window when plotting your slope field to zoom in on any possibly horizontal slopes.)
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