# Aim How do we solve vector problems mathematically

Aim: How do we solve vector problems mathematically? HW:

How do we break down vectors into x & y components? X&Y X (Horizontal) Y (Vertical)

Station Activity • Go to the station assigned and work with a partner on the given question.

A sailboat travels East across water with a velocity of 5 m/s. At the same time there is a wind blowing 2 m/s South. What is the boats resultant velocity?

A rocket travels 35 degrees North of West with an acceleration of 2 m/s. What is the x and y component of it’s motion?

Vector Addition To calculate a vector by vector addition… 1. Break known vectors into components. 2. Combine similar (same direction) components. 3. Use pythagorean theorem to combine horizontal and vertical components. 4. Calculate the direction (angle) with SOHCAHTOA.

Mailman Richard leaves the post office and drives 22. 0 km in a Northernly direction. He then drives in a direction 60. 0 o South of East for 47. 0 km. What is his displacement from the post office?

Mailman Richard Lets try to calculate the resultant mathematically! Y-Component • 22 km N & -47 Sin(60 o) km X-Component • 47 Cos(60 o) km Now What? • Total Y = -18. 7 km • Total X = 23. 5 km Resultant? • D 2 x+D 2 y = D 2 Angle? (TOA)

What do we remember about vectors? Write all key terms related Vectorsto solving vector problems. • Magnitude & Direction • Resultant: Sum of vectors • Write your own • Equilibrium Force problem for the class. • Head to Tail Method • Break into x & y components… why? ? ? • Use Pythagorean Theorem to add components. • Use TOA for angle

Summary With Forces Using the triple force scales, what happens when everyone is pulling, but nobody moves? • Equilibrium • If we are asked to subtract vectors, this means we add vectors for the opposite direction. • V 1 – V 2 = V 1 + (-V 2) What is the equilibrium force for the two students pulling?

- Slides: 10