vector problems - north hunterdon-voorhees regional high ... · vector problems . general...
TRANSCRIPT
![Page 1: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/1.jpg)
Vector Problems
![Page 2: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/2.jpg)
General Information
• Vectors act independently
• Example: A boat with a velocity of 20 m/s east
and a 7 m/s current flowing south.
– The boat travels 20 m east every second
– The river flows south 7 m each second
– If the boat were not going east it would be carried
by the current in the same way it gets carried by
the current when it is drifting
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Vector Addition Reminders
• Vectors are drawn as arrows
• Always combine vectors tail to head
• You can move a vector so long as you don’t change its magnitude or direction
• The resultant is drawn from the tail of the first vector to the head of the last vector
• The angle you are looking at is the angle formed by the tail of the first vector and the tail of the resultant
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Vector Mathematics
• Always draw a diagram
• Use the Pythagorean Theorem for the magnitude of
the resultant
• Use tangent for the size of the angle
• Make sure you accurately describe the exact
direction of the resultant
• Resultants have two parts
– Magnitude with unit
– Angle with reference degree
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1. A boat travels west at a speed of 24 m/s across a river that is
flowing south at 9 m/s. What is the resultant velocity of the boat?
![Page 6: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/6.jpg)
Vector Diagram
![Page 7: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/7.jpg)
Magnitude Calculation
6.2565781576924 22 c
![Page 8: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/8.jpg)
Angle Calculation
6.20375.024
9tan 1
![Page 9: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/9.jpg)
Final Answer
25.6 m/s @ 249.4°
![Page 10: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/10.jpg)
2. A plane flies south at 650 mph with a cross wind towards the east at 130 mph. What
is the resultant velocity of the plane?
![Page 11: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/11.jpg)
Vector Diagram
![Page 12: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/12.jpg)
Magnitude Calculation
2 2650 130 422500 16900 439400 663c
![Page 13: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/13.jpg)
Angle Calculation
3.112.0650
130tan 1
![Page 14: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/14.jpg)
Final Answer
662.9 mph @ 169°
![Page 15: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/15.jpg)
3. An airplane flying east at 310 m/s has a 45 m/s
tailwind. What is the resultant velocity of the plane?
![Page 16: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/16.jpg)
Vector Diagram
![Page 17: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/17.jpg)
Magnitude Calculation
c = 310 + 45 = 355
![Page 18: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/18.jpg)
Angle Calculation
Everything is headed east
![Page 19: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/19.jpg)
Final Answer
355 m/s @ 90°
![Page 20: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/20.jpg)
4. The Antarctic expedition drives their snowmobiles 185 miles
south from their camp. Then they turn and drive 70 miles west.
Now it is time to return to camp. In what direction must they
drive and will they make it on 190 miles worth of gas?
![Page 21: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/21.jpg)
Vector Diagram
• Note that this is a
special case where the
resultant vector appears
to point backwards.
• This is because that is
the path they will need
to take back to their
base.
![Page 22: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/22.jpg)
Magnitude Calculation
1983912549003422570185 22 c
![Page 23: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/23.jpg)
Angle Calculation
3.6964.270
185tan 1
![Page 24: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/24.jpg)
Final Answer
20.8° & No, they will have to walk 8 miles
![Page 25: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/25.jpg)
5. Tarzan is swimming east at 2.4 m/s across a river
that is 1660 meters wide and flows north at 5.2 m/s.
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Vector Diagram
![Page 27: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/27.jpg)
Magnitude Calculation
73.58.3204.2776.52.54.2 22 c
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Angle Calculation
2.6517.24.2
2.5tan 1
![Page 29: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/29.jpg)
Final Answer
5.73 m/s @ 24.8°
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B. How long will it take him to cross the river?
• Data
• Equation
• Math
• Answer
• d = 1660 m
va = 2.4 m/s
• t = d ÷ va
• t = 1660 ÷ 2.4
• t = 692 s
![Page 31: Vector Problems - North Hunterdon-Voorhees Regional High ... · Vector Problems . General Information • Vectors act independently • Example: A boat with a velocity of 20 m/s east](https://reader033.vdocuments.site/reader033/viewer/2022041715/5e4ac27fb72b1605050ed97e/html5/thumbnails/31.jpg)
C. How far downstream will he end up?
• Data
• Equation
• Math
• Answer
• t = 692 s
va = 5.2 m/s
• d = va × t
• d = 692 × 5.2
• d = 3600 m
(or about 2.5 miles)