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**Unformatted text preview: **.030 0 kg/s. (a) Calculate the terminal speed of the
leaf. (b) Use Euler ’s method of numerical analysis to
ﬁnd the speed and position of the leaf as functions of 177 Problems WEB time, from the instant it is released until 99% of terminal speed is reached. (Hint: Try t 0.005 s.)
41. A hailstone of mass 4.80 10 4 kg falls through the air
and experiences a net force given by
F 42. 43. 44. 45. mg Cv 2 where C 2.50 10 5 kg/m. (a) Calculate the terminal speed of the hailstone. (b) Use Euler ’s method of
numerical analysis to ﬁnd the speed and position of the
hailstone at 0.2-s intervals, taking the initial speed to be
zero. Continue the calculation until the hailstone
reaches 99% of terminal speed.
A 0.142-kg baseball has a terminal speed of 42.5 m/s
(95 mi/h). (a) If a baseball experiences a drag force of
magnitude R Cv 2, what is the value of the constant C ?
(b) What is the magnitude of the drag force when the
speed of the baseball is 36.0 m/s? (c) Use a computer
to determine the motion of a baseball thrown vertically
upward at an initial speed of 36.0 m/s. What maximum height does the ball reach? How long is it in
the air? What is its speed just before it hits the ground?
A 50.0-kg parachutist jumps from an airplane and falls
with a drag force proportional to the square of the
speed R Cv 2. Take C 0.200 kg/m with the parachute closed and C 20.0 kg/m with the chute open.
(a) Determine the terminal speed of the parachutist in
both conﬁgurations, before and after the chute is
opened. (b) Set up a numerical analysis of the motion
and compute the speed and position as functions of
time, assuming the jumper begins the descent at
1 000 m above the ground and is in free fall for 10.0 s
before opening the parachute. (Hint: When the parachute opens, a sudden large acceleration takes place; a
smaller time step may be necessary in this region.)
Consider a 10.0-kg projectile launched with an initial
speed of 100 m/s, at an angle of 35.0° elevation. The resistive force is R
b v, where b 10.0 kg/s. (a) Use a
numerical method to determine the horizontal and vertical positions of the projectile as functions of time.
(b) What is the range of this projectile? (c) Determine
the elevation angle that gives the maximum range for
the projectile. (Hint: Adjust the elevation angle by trial
and error to ﬁnd the greatest range.)
A professional golfer hits a golf ball of mass 46.0 g with
her 5-iron, and the ball ﬁrst strikes the ground 155 m
(170 yards) away. The ball experiences a drag force of
magnitude R Cv 2 and has a terminal speed of
44.0 m/s. (a) Calculate the drag constant C for the golf
ball. (b) Use a numerical method to analyze the trajectory of this shot. If the initial velocity of the ball makes
an angle of 31.0° (the loft angle) with the horizontal,
what initial speed must the ball have to reach the 155-m
distance? (c) If the same golfer hits the ball with her 9iron (47.0° loft) and it ﬁrst strikes the ground 119 m
away, what is the initial speed of...

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