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Problems 331

rifle, used for hunting deer, fires a bullet of 90 grains (1 grain 16. Two automobiles, moving at 65 km/h in opposite directions,
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is 7000 lb) with a speed of 975 m/s. A Remington .35 rifle fires collide head-on. One automobile has a mass of 700 kg; the
a bullet of 200 grains with a speed of 674 m/s. What is the other, a mass of 1500 kg. After the collision, both remain
momentum of each bullet? joined together. What is the velocity of the wreck? What is
5. An electron, of mass 9.1 10 31 kg, is moving in the x–y the change of the velocity of each automobile during the
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plane; its speed is 2.0 10 m/s, and its direction of motion collision?
makes an angle of 25 with the x axis. What are the compo- 17. The nucleus of an atom of radium (mass 3.77 10 25 kg)
nents of the momentum of the electron? suddenly ejects an alpha particle (mass 6.68 10 27 kg) of
6. A skydiver of mass 75 kg is in free fall. What is the rate of an energy of 7.26 10 16 J. What is the velocity of the
change of his momentum? Ignore friction. recoil of the nucleus? What is the kinetic energy of the
recoil?
7. A soccer player kicks a ball and sends it flying with an initial
speed of 26 m/s at an upward angle of 30 . The mass of the 18. A lion of mass 120 kg leaps at a hunter with a horizontal
ball is 0.43 kg. Ignore friction. velocity of 12 m/s. The hunter has an automatic rifle firing
bullets of mass 15 g with a muzzle speed of 630 m/s, and he
(a) What is the initial momentum of the ball?
attempts to stop the lion in midair. How many bullets would
(b) What is the momentum when the ball reaches maximum the hunter have to fire into the lion to stop its horizontal
height on its trajectory? motion? Assume the bullets stick inside the lion.
(c) What is the momentum when the ball returns to the *19. Find the recoil velocity for the gun described in Example 2 if
ground? Is this final momentum the same as the initial the gun is fired with an elevation angle of 20 .
momentum?
*20. Consider the collision between the moving and the initially
8. The Earth moves around the Sun in a circle of radius 1.5 stationary automobiles described in Example 3. In this exam-
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10 m at a speed of 3.0 10 m/s. The mass of the Earth is ple we neglected effects of the friction force exerted by the
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6.0 10 kg. Calculate the magnitude of the rate of change road during the collision. Suppose that the collision lasts for
of the momentum of the Earth from these data. (Hint: The 0.020 s, and suppose that during this time interval the joined
magnitude of the momentum does not change, but the direc- automobiles are sliding with locked wheels on the pavement
tion does.) with a coefficient of friction 0.90. What change of
k
9. A 1.0-kg mass is released from rest and falls freely. How much momentum and what change of speed does the friction force
momentum does it acquire after one second? After ten seconds? produce in the joined automobiles in the interval of 0.020 s? Is
10. A 55-kg woman in a 20-kg rowboat throws a 3.0-kg life pre- this change of speed significant?
server with a horizontal velocity of 5.0 m/s. What is the recoil *21. A Maxim machine gun fires 450 bullets per minute. Each
velocity of the woman and rowboat? bullet has a mass of 14 g and a velocity of 630 m/s.
11. A 90-kg man dives from a 20-kg boat with an initial horizon- (a) What is the average force that the impact of these bullets
tal velocity of 2.0 m/s (relative to the water). What is the ini- exerts on a target? Assume that the bullets penetrate the
tial recoil velocity of the boat? (Neglect water friction.) target and remain embedded in it.
12. A hydrogen atom (mass 1.67 10 27 kg) at rest can emit a (b) What is the average rate at which the bullets deliver their
photon (a particle of light) with maximum momentum 7.25 energy to the target?
10 27 kg m/s. What is the maximum recoil velocity of the *22. An owl flies parallel to the ground and grabs a stationary
hydrogen atom? mouse with its talons. The mass of the owl is 250 g, and that
13. Calculate the change of the kinetic energy in the collision of the mouse is 50 g. If the owl’s speed was 4.0 m/s before
between the two automobiles described in Example 3. grabbing the mouse, what is its speed just after the capture?
14. A rifle of 10 kg lying on a smooth table discharges acciden- *23. A particle moves along the x axis under the influence of a
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tally and fires a bullet of mass 15 g with a muzzle speed of 650 time-dependent force of the form F 2.0t 3.0t , where F x
x
m/s. What is the recoil velocity of the rifle? What is the is in newtons and t is in seconds. What is the change in
kinetic energy of the bullet, and what is the recoil kinetic momentum of the particle between t 0 and t 5.0 s?
energy of the rifle? [Hint: Rewrite Eq. (10.3) as dp F dt and integrate.]
x
x
15. A typical warship built around 1800 (such as the USS *24. A vase falls off a table and hits a smooth floor, shattering into
Constitution) carried 15 long guns on each side. The guns fired three fragments of equal mass which move away horizontally
a shot of 11 kg with a muzzle speed of about 490 m/s. The along the floor. Two of the fragments leave the point of impact
mass of the ship was about 4000 metric tons. Suppose that all with velocities of equal magnitudes v at right angles. What are
of the 15 guns on one side of the ship are fired (almost) simul- the magnitude and direction of the horizontal velocity of the
taneously in a horizontal direction at right angle to the ship. third fragment? (Hint: The x and y components of the
What is the recoil velocity of the ship? Ignore the resistance momentum are conserved separately.)
offered by the water.