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Chapter 2: Problem 22
A giant eruption on the Sun propels solar material from rest to \(450 \mathrm{km} / \mathrm{s}\) over a period of \(1 \mathrm{h} .\) Find the average acceleration.
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You're an investigator for the National Transportation Safety Board, examining a subway accident in which a train going at \(80 \mathrm{km} / \mathrm{h}\) collided with a slower train traveling in the same direction at \(25 \mathrm{km} / \mathrm{h}\). Your job is to determine the relative speed of the collision, to help establish new crash standards. The faster train's "black box" shows that it began negatively accelerating at \(2.1 \mathrm{m} / \mathrm{s}^{2}\) when it was \(50 \mathrm{m}\) from the slower train, while the slower train continued at constant speed. What do you report?
An object starts moving in a straight line from position \(x_{0},\) at time \(t=0,\) with velocity \(v_{0} .\) Its acceleration is given by \(a=a_{0}+b t,\) where \(a_{0}\) and \(b\) are constants. Find expressions for (a) the instantaneous velocity and (b) the position, as functions of time.
You're at mission control for a rocket launch, deciding whether to let the launch proceed. A band of clouds \(5.3 \mathrm{km}\) thick extends upward from \(1.9 \mathrm{km}\) altitude. The rocket will accelerate at \(4.6 \mathrm{m} / \mathrm{s}^{2},\) and it isn't allowed to be out of sight for more than \(30 \mathrm{s}\) Should you allow the launch?
Ice skaters, ballet dancers, and basketball players executing vertical leaps often give the illusion of "hanging" almost motionless near the top of the leap. To see why this is, consider a leap to maximum height \(h .\) Of the total time spent in the air, what fraction is spent in the upper half (i.e., at \(y>\frac{1}{2} h\) )?
A balloon is rising at \(10 \mathrm{m} / \mathrm{s}\) when its passenger throws a ball straight up at \(12 \mathrm{m} / \mathrm{s}\) relative to the balloon. How much later does the passenger catch the ball?
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