(III) A lifeguard standing at the side of a swimming pool spots a child in distress, Fig. 2–53. The lifeguard runs with average speed υ R along the pool’s edge for a distance x , then jumps into the pool and swims with average speed υ S on a straight path to the child, ( a ) Show that the total time t it takes the lifeguard to get to the child is given by t = x υ R + D 2 + ( d − x ) 2 υ S . ( b ) Assume υ R = 4.0 m/s and υ S = 1.5m/s. Use a graphing calculator or computer to plot t vs. x in part ( a ), and from this plot determine the optimal distance x the life-guard should run before jumping into the pool (that is, find the value of x that minimizes the time t to get to the child).
(III) A lifeguard standing at the side of a swimming pool spots a child in distress, Fig. 2–53. The lifeguard runs with average speed υ R along the pool’s edge for a distance x , then jumps into the pool and swims with average speed υ S on a straight path to the child, ( a ) Show that the total time t it takes the lifeguard to get to the child is given by t = x υ R + D 2 + ( d − x ) 2 υ S . ( b ) Assume υ R = 4.0 m/s and υ S = 1.5m/s. Use a graphing calculator or computer to plot t vs. x in part ( a ), and from this plot determine the optimal distance x the life-guard should run before jumping into the pool (that is, find the value of x that minimizes the time t to get to the child).
(III) A lifeguard standing at the side of a swimming pool spots a child in distress, Fig. 2–53. The lifeguard runs with average speed
υ
R
along the pool’s edge for a distance x, then jumps into the pool and swims with average speed
υ
S
on a straight path to the child, (a) Show that the total time t it takes the lifeguard to get to the child is given by
t
=
x
υ
R
+
D
2
+
(
d
−
x
)
2
υ
S
.
(b) Assume
υ
R
= 4.0 m/s and
υ
S
= 1.5m/s. Use a graphing calculator or computer to plot t vs. x in part (a), and from this plot determine the optimal distance x the life-guard should run before jumping into the pool (that is, find the value of x that minimizes the time t to get to the child).
A person driving her car at 35 km/h approaches an inter-
section just as the traffic light turns yellow. She knows that
the yellow light lasts only 2.0s before turning to red, and
she is 28 m away from the near side of the intersection
(Fig. 2–49). Should she try to stop, or should she speed up
to cross the intersection before the light turns red? The
intersection is 15 m wide. Her car's maximum deceleration
is -5.8 m/s?, whereas it can accelerate from 45 km/h to
65 km/h in 6.0 s. Ignore the length of her car and her
reaction time.
– 28 m -
-15 m→
FIGURE 2-49 Problem 73.
In putting, the force with which a golfer strikes a ball is
planned so that the ball will stop within some small distance
of the cup, say 1.0m long or short, in case the putt is missed.
Accomplishing this from an uphill lie (that is, putting the
ball downhill, see Fig. 2–47) is more difficult than from a
downhill lie. To see why, assume that on a particular green
the ball decelerates constantly at 1.8 m/s² going downhill,
and constantly at 2.6 m/s² going uphill. Suppose we have an
uphill lie 7.0 m from the cup. Calculate the allowable range
of initial velocities we may impart to the ball so that it stops
in the range 1.0 m short to 1.0 m long of the cup. Do the
same for a downhill lie 7.0 m from the cup. What in your
results suggests that the downhill putt is more difficult?
Uphill
lie
Downhill
7.0 m
lie
- 7.0 m
FIGURE 2-47 Problem 70.
(b) A particle moves with position y = 2x , where x and y are in meters. The velocity in
x direction is v, = 31² . Determine the velocity at time t = 5 s and write in unit vectors.
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