1. practice ‘c’ p. 94 #’s 1, 2 & 3

2. 1. A football player runs directly down the field for 35 m before turning to the right at an angle of 25° from his original direction and running an additional 15 m before getting tackled. What is the magnitude and direction of the runner’s total displacement?
35 m
25o
15 m
sin Θ = opposite = y
hypotenuse h
cos Θ = adjacent = x
hypotenuse h
y = (h)(sin Θ)
= (15 m) (sin25)
= (15 m) (.423)
= m
x = (h)(cos Θ)
=(15 m) (cos 25)
= (15 m) (.906)
= m

3. Now find the resultant of a NEW triangle
tan Θ = opp
adj
Pyth theorem:
h2 = x2 + y2 Θ
= 6.3 m = = 7o
48.6 m
h2 = (48.6 m)2 + (6.3 m)2
h2 = m m2
35 m m = m = x
h2 = 2401 m2
Θ ??
25o
6.3 m = y
49 m
h = 49 m
h = 49 m to the right of
downfield at 7o

4. 2. A plane travels 2.5 km at an angle of 35° to the ground and then changes direction and travels 5.2 km at an angle of 22° to the ground. What is the magnitude and direction of the plane’s total displacement?
5.2 km
22o
2.5 km
35o

5. 2. A plane travels 2.5 km at an angle of 35° to the ground and then changes direction and travels 5.2 km at an angle of 22° to the ground. What is the magnitude and direction of the plane’s total displacement?
For the 1st “leg”
5.2 km
22o
cos Θ = adjacent = x
hypotenuse h
2.5 km
35o
x = h cos Θ
= (2.5 km) (cos 35)
= (2.5 km) (.819)
= 2 km
sin Θ = opposite = y
hypotenuse h
y = h sin Θ
= (2.5 km) (sin 35)
= (2.5 km) (.574)
= 1.4 km

6. Need to find resultant magnitude & direction
2. A plane travels 2.5 km at an angle of 35° to the ground and then changes direction and travels 5.2 km at an angle of 22° to the ground. What is the magnitude and direction of the plane’s total displacement?
For the 2nd “leg”
5.2 km
22o
cos Θ = adjacent = x
hypotenuse h
2.4 km
35o
x = h cos Θ
= (5.2 km) (cos 22)
= (5.2 km) (.927)
= km
sin Θ = opposite = y
hypotenuse h
y = h sin Θ
= (5.2 km) (sin 22)
= (5.2 km) (.375)
= 1.95 km
Need to find resultant magnitude & direction

7. h = 7.6 km = Θ h2 = x2 + y2 h2 = (6.82 km)2 + (3.35 km)2
2. A plane travels 2.5 km at an angle of 35° to the ground and then changes direction and travels 5.2 km at an angle of 22° to the ground. What is the magnitude and direction of the plane’s total displacement?
For the final resultant h
5.2 km
22o
2.4 km
y = 1.4 km + =
3.35 km Θ
h2 = x2 + y2
2 km +
4.82 km = x
h2 = (6.82 km)2 + (3.35 km)2
6.82 km = x
h2 = 47 km km2
h2 = 58 km2
h = 7.6 km =

8. For Θ Θ = 26o above the horizon h = 7.6 km
2. A plane travels 2.5 km at an angle of 35° to the ground and then changes direction and travels 5.2 km at an angle of 22° to the ground. What is the magnitude and direction of the plane’s total displacement?
5.2 km
22o
For Θ
2.4 km
y = km Θ
tan Θ = opp
adj
6.78 km = x
Θ = tan -1 opp
adj
Θ = 26o above the horizon
Θ = tan km = .4911
6.82 km
h = 7.6 km

9. 3. During a rodeo, a clown runs 8
3. During a rodeo, a clown runs 8.0 m north, turns 55° north of east, and runs 3.5 m. Then, after waiting for the bull to come near, the clown turns due east and runs 5.0 m to exit the arena. What is the clown’s total displacement?
5 m
3.5 m
For the 2nd vector:
55o
x = h cos Θ
= (3.5 m) (cos 55)
= (3.5 m) (.574)
= 2 m
8 m
cos Θ = adjacent = x
hypotenuse h
y = h sin Θ
= (3.5 m) (sin 55)
= (3.5 m) (.819)
= m
sin Θ = opposite = y
hypotenuse h

10. h2 = x2 + y2 h2 = (7 m)2 + (10.9 m)2 h2 = 49 m2 + 121 m2 h2 = 170 m2
3. During a rodeo, a clown runs 8.0 m north, turns 55° north of east, and runs 3.5 m. Then, after waiting for the bull to come near, the clown turns due east and runs 5.0 m to exit the arena. What is the clown’s total displacement?
h = 13 m
h2 = x2 + y2
2 m +
5 m = 7 m = x
h2 = (7 m)2 + (10.9 m)2
55o
h2 = 49 m m2
h2 = 170 m2

11. h2 = x2 + y2 h2 = (7 m)2 + (10.9 m)2 h2 = 49 m2 + 121 m2 h2 = 170 m2
3. During a rodeo, a clown runs 8.0 m north, turns 55° north of east, and runs 3.5 m. Then, after waiting for the bull to come near, the clown turns due east and runs 5.0 m to exit the arena. What is the clown’s total displacement?
Use the x & y vectors
to find resultant h:
2 m +
5 m = 7 m = x
h2 = x2 + y2
55o
h2 = (7 m)2 + (10.9 m)2
8m m = 10.9 m = y
h2 = 49 m m2
h = 13 m
h2 = 170 m2

12. 3. During a rodeo, a clown runs 8
3. During a rodeo, a clown runs 8.0 m north, turns 55° north of east, and runs 3.5 m. Then, after waiting for the bull to come near, the clown turns due east and runs 5.0 m to exit the arena. What is the clown’s total displacement?
For Θ use the vectors…
Θ = tan -1 opp
adj
h = 13 m
55o
10.9 m = y
= 10.9 m = = 57o
7 m Θ
7 m = x
Θ = 57o north of east