Chapter 3 – Vectors & Projectile Motion

Vocab Scalar Vector Resultant Component Resolve

Combining Vectors Arrange vectors head to tail; head to tail Result is from first tail to last head Length is found by Pythagorean theorem a2 + b2 = c2

Practice combining vectors 5.0 m/s north with 12 m/s west 6.0 m/s south with 8.0 m/s west 3.0 m/s northwest with 4.0 m/s northeast 12 m/s southeast with 9.0 m/s northwest

Resolving Vectors Any vector can be resolved into 2 perpendicular vectors (components) Use angle and trigonometry functions to find components (5.0N)sin(30) 5.0 N 30’ (5.0N)cos(30)

Practice resolving vectors A 25 Newton force is dragging a wagon at 25° from the horizontal A 16 Newton wind is blowing the sailboat at 35° west of north You pull up on the desk with a force of 16 Newtons at an angle of 10° above horizontal

Component vector independence Perpendicular vectors are completely independent of each other This is why we resolve vectors, we can treat each piece individually

Complex combinations When vectors aren’t perpendicular Resolve all vectors Combine all vertical parts Combine all horizontal parts Combine vertical and horizontal results Works for more than 2 vectors

Practice combining complex vectors A 25 N 20.° north of west with 14 N 15° south of west A 12 N 25.° above the horizontal with 18 N 55° above the horizontal A 30. N 30.° west of north with 16 N 15° south of west with 41 N 5° east of south.

Upwardly Launched Projectiles Because gravity acts on projectiles, the projectile follows a curved path and hits the ground.

Upwardly Launched Projectiles If no gravity acted on the object, the object would follow a straight line path. It falls the same vertical distance that it would if it were dropped from rest. 1s? 3s?

What angle of launch is best? Best angle – Compliment angles- Real world best –

Frames of Reference The same motion appears different from different frames of reference Car examples – orbiting examples Video of plane, snowmobile Pirate problem