(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).
- (II) A child, who is 45 m from the bank of a river, is being
carried helplessly downstream by the river's swift current
of 1.0 m/s. As the child passes a lifeguard on the river's
bank, the lifeguard starts swimming in a straight line
(Fig. 3–46) until she reaches the child at a point downstream.
If the lifeguard can swim at a speed of 2.0 m/s relative
to the water, how long does it take her to reach the child?
How far downstream does the lifeguard intercept the
child?
1.0 m/s
2.0 m/s
- 45 m
FIGURE 3-46 Problem 49.
(III) Two cars approach a street corner at right angles to
each other (Fig. 3–47). Car 1 travels at a speed relative
to Earth vIE = 35 km/h, and car 2 at v2E = 55 km/h.
What is the relative
2
velocity of car 1 as
seen by car 2? What
is the velocity of car 2
relative to car 1?
2E
1E
FIGURE 3-47
Problem 51.
(II) Extreme-sports enthusiasts have been known to jump
off the top of El Capitan, a sheer granite cliff of height
910 m in Yosemite National Park. Assume a jumper runs
horizontally off the top of El Capitan with speed 4.0 m/s
and enjoys a free fall until she is 150 m above the valley
floor, at which time she opens her parachute (Fig. 3–37).
(a) How long is the jumper in free fall? Ignore air resis-
tance. (b) It is important to be as far away from the cliff
as possible before opening the parachute. How far from
the cliff is this jumper when she opens her chute?
4.0 m/s
910 m
150 m
FIGURE 3-37
Problem 26.
Chapter 2 Solutions
Physics for Scientists and Engineers with Modern Physics
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