17 A ball is released from a great height so that it falls vertically downwards towards the surface of the Earth.
17
- Using a simple model, Andy predicts that the velocity of the ball, exactly 2 seconds after being released from rest, is \(2 g \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
Show how Andy has obtained his prediction.
17 - Using a refined model, Amy predicts that the ball's acceleration, \(a \mathrm {~ms} ^ { - 2 }\), at time \(t\) seconds after being released from rest is
$$a = g - 0.1 v$$
where \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is the velocity of the ball at time \(t\) seconds.
Find an expression for \(v\) in terms of \(t\).
17 - Comment on the value of \(v\) for the two models as \(t\) becomes large.