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Chapter 9: Problem 96
The component of the ball's velocity whose magnitude is most affected by the collisions is a. horizontal. b. vertical. c. Both are affected equally.
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High-speed photos of a \(220-\mu \mathrm{g}\) flea jumping vertically show that the jump lasts \(1.2 \mathrm{~ms}\) and involves an average vertical acceleration of \(100 \mathrm{~g}\). What (a) average force and (b) impulse does the ground exert on the flea during its jump? (c) What's the change in the flea's momentum during its jump?
Two objects moving in opposite directions with the same speed \(v\) undergo a totally inelastic collision, and two-thirds of the initial kinetic energy is lost. Find the ratio of their masses.
A neutron (mass \(1.01 \mathrm{u}\) ) strikes a deuteron (mass \(2.01 \mathrm{u}\) ), and they combine to form a tritium nucleus (mass \(3.02 \mathrm{u}\) ). If the neutron's initial velocity was \(23.5 \hat{\imath}+14.4 \hat{\jmath} \mathrm{Mm} / \mathrm{s}\) and if the tritium leaves the reaction with velocity \(15.1 \hat{\imath}+22.6 \hat{\jmath} \mathrm{Mm} / \mathrm{s}\), what was the deuteron's velocity?
A \(55-\mathrm{kg}\) sprinter stands on the left end of a \(180-\mathrm{kg}\) cart moving leftward at \(6.9 \mathrm{~m} / \mathrm{s}\). She runs to the right end and continues horizontally off the cart. What should be her speed relative to the cart so that once she's off the cart she has no horizontal velocity relative to the ground?
A rocket of mass \(M\) moving at speed \(v\) ejects an infinitesimal mass \(d m\) out its exhaust nozzle at speed \(v_{\text {ex }}\). (a) Show that conservation of momentum implies that \(M d v=v_{\text {ex }} d m\), where \(d v\) is the change in the rocket's speed. (b) Integrate this equation from some initial speed \(v_{\mathrm{i}}\) and mass \(M_{\mathrm{i}}\) to a final speed \(v_{\mathrm{f}}\) and mass \(M_{\mathrm{f}}\) to show that the rocket's final velocity is given by the expression \(v_{\mathrm{f}}=v_{\mathrm{i}}+v_{\mathrm{ex}} \ln \left(M_{\mathrm{i}} / M_{\mathrm{f}}\right)\).
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