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/s V = ? Use the Pythagorean Theorem to find the size of V… V 2 = V =  ( ) = 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?