Comparison

Question 1

Expand in a Taylor series about the point t=0 retaining the first two terms of the series. Show that eqn. (3.4) reduces to eqn (6.2) when k/m << 1.

Question 2

Plot eqns. (2.5) and (4.1) for the distances between 0 and 3500 m with k = 0.2 Ns2/m2 and m = 80 kg and note how badly eqn. (2.5) correlates with eqn (4.1) for the skydiver as the distance increases.

Question 3

a. Make a plot of [v(t) - vf(t)]] for the skydiver (k = 0.2 Ns2/m2 and m = 80 kg) as a function of time for times from 0 to 10 s.

b. What does this plot tell you about the difference between Falling in a Fluid vs. Falling in a Vacuum? How do you explain the shape of the plot for small t? for large t?

Question 4

The plot of (v - vf) vs. t shows that vf becomes constant for large t. Determine the time required for vf to be equal to :. (k = 0.2 Ns2/m2 and m = 80 kg)

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