Name: _______________________________ Date: ___________ Class: ___________
Practice – Solve the following problems mathematically, including magnitude and direction.
All problems should have vectors drawn with them.
1. Calculate the resultant velocity of an airplane that normally flies at 200 km/h if it
encounters a 50-km/h tailwind. If it encounters a 50-km/h headwind.
Tailwind:
Headwind:
200 km/h
50 km/h
Resultant = 250 km/h
Resultant = 150 km/h
2. Calculate the resultant of the pair of velocities 100 km/h north and 75 km/h south.
Calculate the resultant if both of the velocities are directed north.
100 km/h
North
75 km/h
South
75 km/h
North
Resultant =
25 km/h North
100 km/h
North
Resultant =
175 km/h
North
3. Calculate the magnitude of the resultant of a pair of 100 km/h velocity vectors that are
at right angles to each other.
100 km/h
a2 + b2 = c2
(100)2 + (100)2 = 20000
√20000 = 141.42 km/h
100 km/h
4. Calculate the magnitude of the horizontal and vertical components of a vector that is
100 units long and is oriented at 45
c=
100 units
45
b
a
sin 𝜃 =
cos 𝜃 =
𝑏
𝑐
𝑎
𝑐
𝑏 = 𝑐 ∗ sin 𝜃 = 100*sin(45) = 70.7 units
𝑎 = 𝑐 ∗ cos 𝜃 = 100*cos(45) = 70.7 units
5. Calculate the resultant of a horizontal vector with a magnitude of 4 units and a vertical
vector with a magnitude of 3 units
c=?
a=4
Schneider
b=3
a2 + b2 = c2
(4)2 + (3)2 = 25
√25 = 5 units
Honors Physics
Name: _______________________________ Date: ___________ Class: ___________
6. What are the horizontal and vertical components of a 10-unit vector that is oriented
37 above the horizontal?
c = 10
37
b
𝑏 = 𝑐 ∗ sin 𝜃 = 10 ∗ sin 37 = 6.02 units
𝑎 = 𝑐 ∗ cos 𝜃 = 10 ∗ cos 37 = 7.99 units
a
7. What are the horizontal and vertical components of a 10-unit vector that is oriented
53 above the horizontal?
c = 10
b
𝑏 = 𝑐 ∗ sin 𝜃 = 10 ∗ sin 53 = 7.99 units
𝑎 = 𝑐 ∗ cos 𝜃 = 10 ∗ cos 53 = 6.02 units
53
a
8. The launching velocity of a projectile is 20 m/s at 53 above the horizontal. What is the
vertical component of its velocity at launch? It’s horizontal component of velocity?
c=
20 m/s
b
𝑏 = 𝑐 ∗ sin 𝜃 = 20 ∗ sin 53 = 16 m/s
𝑎 = 𝑐 ∗ cos 𝜃 = 10 ∗ cos 53 = 12 m/s
53
a
Schneider
Honors Physics