1. Vector Worksheet 3 Answers
1. A box is being pulled across the floor by a rope at an angle
of 50o to the horizontal. The tension in the rope is 100 N.
(a) Find Fh, the horizontal component of the force on the rope.
100 N Fv
50o Fh Fh
100
100
cos 50 =
100
Fh = 100 cos 50
= Fh = N

2. 1. A box is being pulled across the floor by a rope at an angle
of 50o to the horizontal. The tension in the rope is 125 N.
(b) Find Fv, the vertical component of the force on the rope.
100 N Fv
50o
64.2 N Fv
100
100
sin 50 =
100
Fv = 100 sin 50
= Fv = N

3. 2. A plane is flying with a speed of 200 m/s at a bearing of 60o.
(a) Determine the eastward component of the velocity. 0o
60o
270o
90o
180o

4. 2. A plane is flying with a speed of 200 m/s at a bearing of 60o.
(a) Determine the eastward component of the velocity.
200 m/s
60o vn
30o ve ve
200
200
cos 30 =
200
ve = 200 cos 30
= ve = 173 m/s

5. 2. A plane is flying with a speed of 200 m/s at a bearing of 60o.
(b) Determine the northward component of the velocity.
200 m/s
60o vn
30o
173 m/s vn
200
200
sin 30 =
200
vn = 200 sin 30
= vn = 100 m/s

6. 2. A plane is flying with a speed of 200 m/s at a bearing of 60o.
(c) How far east has the plane flown in 10 seconds?
200 m/s
60o
100 m/s
30o
173 m/s
d = v t
de = ve t
= ( 173 m/s )( 10 s )
de = m

7. 3. A plane is flying at a speed of 500 km/hr at a bearing of
240o. Find the westward component of the plane’s velocity. 0o
270o
90o
30o
180o
500 km/hr
at 240o

8. 3. A plane is flying at a speed of 525 km/hr at a bearing of
240o. Find the westward component of the plane’s velocity. vw
vw = 500 cos 240 ?
30o
vw = m/s
60o vw
500 km/hr vw
500 vw
500
500
cos 30 =
500
sin 60 =
500
500
vw = 500 cos 30
vw = 500 sin 60
vw = 433 km/hr
vw = 433 km/hr

9. 4. A rope is tied to a box on the floor and is held at angle of
60o to the horizontal. The box has a mass of 6.0 kg. A force
of 100 N is exerted on the box via the rope.
(a) Determine the vertical component of the force. Fv
100
100 N Fv
100
sin 60 =
100
60o
6.0 kg Fh
Fv = 100 sin 60
Fv = 87 N

10. 4. A rope is tied to a box on the floor and is held at angle of
60o to the horizontal. The box has a mass of 6.0 kg. A force
of 85 N is exerted on the box via the rope.
(b) Does the box stay on the floor, or is it pulled off the
floor by the force? (Compare weight with Fv )
Wt. = m g
100 N
87 N
= ( 6.0 kg )( 9.8 m/s2 )
60o
Wt. = 59 N
6.0 kg Fh
Fv > Wt.
Box pulled off floor
Wt.