(I) Huck Finn walks at a speed of 0.70m/s across his raft (that is, he walks perpendicular to the raft’s motion relative to the shore). The raft is traveling down the Mississippi River at a speed of 1.50 m/s relative to the river bank (Fig. 3-49). What is Huck’s velocity (speed and direction) relative to the river bank? FIGURE 3-49 Problem 58. 58. Call the direction of the flow of the river the x direction, and the direction of Huck walking relative to the raft the y direction. v → Huck rel . bank = v → Huck rel . raft + v → raft rel . bank = 0.70 j ^ m/s + 1 .50 i ^ m/s = ( 1.50 i ^ + 0.70 j ^ ) m/s Magnitude: v Huck rel . bank = 1.50 2 + 0.70 2 = 1.66 m/s Direction: θ =tan − 1 0.70 1.50 = 25 ° relative to river
(I) Huck Finn walks at a speed of 0.70m/s across his raft (that is, he walks perpendicular to the raft’s motion relative to the shore). The raft is traveling down the Mississippi River at a speed of 1.50 m/s relative to the river bank (Fig. 3-49). What is Huck’s velocity (speed and direction) relative to the river bank? FIGURE 3-49 Problem 58. 58. Call the direction of the flow of the river the x direction, and the direction of Huck walking relative to the raft the y direction. v → Huck rel . bank = v → Huck rel . raft + v → raft rel . bank = 0.70 j ^ m/s + 1 .50 i ^ m/s = ( 1.50 i ^ + 0.70 j ^ ) m/s Magnitude: v Huck rel . bank = 1.50 2 + 0.70 2 = 1.66 m/s Direction: θ =tan − 1 0.70 1.50 = 25 ° relative to river
(I) Huck Finn walks at a speed of 0.70m/s across his raft (that is, he walks perpendicular to the raft’s motion relative to the shore). The raft is traveling down the Mississippi River at a speed of 1.50 m/s relative to the river bank (Fig. 3-49). What is Huck’s velocity (speed and direction) relative to the river bank?
FIGURE 3-49
Problem 58.
58. Call the direction of the flow of the river the x direction, and the direction of Huck walking relative to the raft the y direction.
v
→
Huck rel
. bank
=
v
→
Huck rel
. raft
+
v
→
raft rel
. bank
=
0.70
j
^
m/s + 1
.50
i
^
m/s
=
(
1.50
i
^
+
0.70
j
^
)
m/s
Magnitude:
v
Huck rel
. bank
=
1.50
2
+
0.70
2
=
1.66
m/s
Direction:
θ
=tan
−
1
0.70
1.50
=
25
°
relative to river
(II) A passenger on a boat moving at 1.70 m/s on a still lake
walks up a flight of stairs at a speed of 0.60 m/s, Fig. 3–43.
The stairs are angled at 45° pointing in the direction of
motion as shown. What is the velocity of the passenger rel-
ative to the water?
0.60 m/s y
45°
V = 1.70 m/s
FIGURE 3-43 Problem 42.
(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.
(I). The motions of two objects, A and B, are defined by the following vectors:
vector A = 6.0622i + 3.500j m/s
vector B = 5.9500i - 10.3057j m/s
unit vector of bullet = -j
Object A and B left at the same time and at the same point. Object A aims to hit object B by firing a bullet in the direction stated above after 20 seconds.
a). What should be the velocity of the bullet so that it will hit object B?
b). What is the distance between object A and B the moment the bullet hits object B?
c). What is the velocity vector of the bullet?
Chapter 3 Solutions
Physics for Scientists and Engineers with Modern Physics
Sears And Zemansky's University Physics With Modern Physics
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