In a game held within a three-dimensional maze, you must move your game piece from start , at xyz coordinates (0, 0, 0), to finish , at coordinates (−2 cm, 4 cm, −4 cm). The game piece can undergo only the displacements (in centimeters) given below. It along the way, the game piece lands at coordinates (−5 cm, −1 cm, −1 cm) or (5 cm, 2 cm, −1 cm), you lose the game. Which displacements and in what sequence will get your game piece to finish ? p → = − 7 i ^ + 2 j ^ − 3 k ^ r → = 2 i ^ − 3 j ^ + 2 k ^ q → = 2 i ^ − j ^ + 4 k ^ s → = 3 i ^ + 5 j ^ − 3 k ^
In a game held within a three-dimensional maze, you must move your game piece from start , at xyz coordinates (0, 0, 0), to finish , at coordinates (−2 cm, 4 cm, −4 cm). The game piece can undergo only the displacements (in centimeters) given below. It along the way, the game piece lands at coordinates (−5 cm, −1 cm, −1 cm) or (5 cm, 2 cm, −1 cm), you lose the game. Which displacements and in what sequence will get your game piece to finish ? p → = − 7 i ^ + 2 j ^ − 3 k ^ r → = 2 i ^ − 3 j ^ + 2 k ^ q → = 2 i ^ − j ^ + 4 k ^ s → = 3 i ^ + 5 j ^ − 3 k ^
In a game held within a three-dimensional maze, you must move your game piece from start, at xyz coordinates (0, 0, 0), to finish, at coordinates (−2 cm, 4 cm, −4 cm). The game piece can undergo only the displacements (in centimeters) given below. It along the way, the game piece lands at coordinates (−5 cm, −1 cm, −1 cm) or (5 cm, 2 cm, −1 cm), you lose the game. Which displacements and in what sequence will get your game piece to finish?
p
→
=
−
7
i
^
+ 2
j
^
−
3
k
^
r
→
=
2
i
^
−
3
j
^
+
2
k
^
q
→
=
2
i
^
−
j
^
+
4
k
^
s
→
=
3
i
^
+ 5
j
^
−
3
k
^
Part C
Find the height yi
from which the rock was launched.
Express your answer in meters to three significant figures.
Learning Goal:
To practice Problem-Solving Strategy 4.1 for projectile motion problems.
A rock thrown with speed 12.0 m/s and launch angle 30.0 ∘ (above the horizontal) travels a horizontal distance of d = 19.0 m before hitting the ground. From what height was the rock thrown? Use the value g = 9.800 m/s2 for the free-fall acceleration.
PROBLEM-SOLVING STRATEGY 4.1 Projectile motion problems
MODEL: Is it reasonable to ignore air resistance? If so, use the projectile motion model.
VISUALIZE: Establish a coordinate system with the x-axis horizontal and the y-axis vertical. Define symbols and identify what the problem is trying to find. For a launch at angle θ, the initial velocity components are vix=v0cosθ and viy=v0sinθ.
SOLVE: The acceleration is known: ax=0 and ay=−g. Thus, the problem becomes one of…
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