5.1-5.3 Vectors

Basic vocabulary…

Vector- quantity described by magnitude and direction

Scalar- quantity described by magnitude only Resultant- sum of vector quantities Components- Vectors that represent the

horizontal and vertical sides of a right triangle with the resultant as the hypotenuse

Calculate the magnitude and direction of a resultant vector.

Use Pythagorean Theorem to find the magnitude (size) of the resultant.

If a and b are two vectors, they can be combined or added. The sum of this is resultant vector c.

Calculate the magnitude and direction of a resultant vector. Use Trigonometry to find the direction of the

resultant.

A boat travels to the North at 15 m/s. The current of the river flows to the west at 7 m/s. What is the resultant velocity of the boat?

7 m/s

15 m/sV = ?

Use the Pythagorean Theorem to find the size of V…

V2 = 72 + 152

V = (49 + 225) = 16.6 m/s

Use trigonometry to figure out the direction…

tan θ = 15/7

θ = tan-1 (15/7)

θ = 65° north of west or… 25 ° west of north or…. 115°****all 3 of these are ways of saying the same direction

Tip to tail sketch…

θ

Resolving vectors into components. Every vector can be visualized as the

hypotenuse of a right triangle. See the red arrows below.

“Resolving a vector” means to find the sides of this right triangle…it’s like working backwards to find the parts that would combine to form the original vector

Resolve vectors into components.

40°

60 N

A projectile is fired at a speed of 28 m/s at a 40° with respect to the horizontal ground. Determine the horizontal and vertical components of the projectiles velocity.

An airplane flies with a speed of 600 km/h in a direction 30° north of west. Find the components of the plane’s velocity.

A boat travels eastward across a river at a speed of 10 m/s. The current of the river runs to the south at 5 m/s. What is the resultant velocity of the boat?

An arrow is moving horizontally at 25 m/s at the same time it is moving upward at 18 m/s. What is the velocity of the arrow at this moment?