1. Examples in Chapter 1

2. Problem 1.42
Vector A has components Ax=1.30 cm and Ay= 2.25 cm; vector B has components Bx=4.10 cm, By=-3.75 cm. Find
The components of the vector sum A+B
the magnitude and direction of A+B
The components of the vector B-A
The magnitude and direction of B-A

3. The components of the vector sum A+B
The sum of the x-components of A and B are equal to the x component of A+B

4. Find the magnitude of A+B
(A+B)y
(A+B)x
(A+B)

5. Find the direction of A+B
(A+B)y
(A+B)x
(A+B) q

6. Components, magnitude and direction of B-A

7. Problem 1.55

8. Your book’s way The book gives 3 formulae for C=AxB
Cx=AyBz-AzBy
Cy=AzBx-AxBz
Cz=AxBy-AyBx
Since A and B have only x- and y- components, we find Cz by
Cz=4*(-2)-5*3=-8-15=-23
||AxB||=23

9. My way: First, a review?
A determinant represents a single number and is used in linear algebra

10. A 3 x 3 determinant

11. For a cross-product

12. For our problem

13. Problem 1.61
Biological tissues are typically made up of 98% water. Given that the density of water is 1 x 103 kg/m3, estimate the mass of
the heart of an adult human
a cell with a diameter of 0.5 mm.
a honey bee.

14. Best guesses
Human heart: size of fist (cylinder 4” long with diameter of 3”)
Honey bee: 1” or 2.5 cm long cylinder with 0.25” diameter

15. Heart Problem 4” = 4*2.54 cm = 10.16 cm or 0.1016 m
Volume of cylinder= p*(d/2)2 *L
p * (7.62/2)2 *10.16=463 cm3 or cc
Note: kg =1 pound

16. Book answer differs by order of magnitude
A cell
Assume spherical!
Volume=4*p/3*(d/2)3
Book answer differs by order of magnitude

17. Honey bee
V=p*(d/2)2 *L=p*(.25/2)2 *1=0.049 in3
Book assumes ½ in long

18. Problem 1.70
A sailor in a small sailboat encounters shifting winds. She sails 2.0 km east then 3.5 km southeast (-450 w.r.t. east) and then an unknown distance. Her final position is 5.8 km directly east of starting point. Find magnitude and direction of the third leg of the journey.

19. Step 1: Draw it!
5.80 km
2.0 km
3.5 km

20. Step 2: Sketch in the details
5.80 km
2.0 km
3.5 km Ay ?

21. Step 3: Simplify
5.80 km-2.0 km=3.8km
2.0 km
3.5 km Ay Ay Ay ?

22. Step 4: Solve 5.80 km-2.0 km=3.8km 2.0 km Ay 3.5 km Ay Ay

23. Step 5: 5.80 km-2.0 km=3.8km 2.0 km Ay 3.5 km Ay=2.47 km Ay
?= =1.33 km=Ax

24. Step 6:
1.33 km
2.47 km q