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Projectile Motion: Vector Quantity Analysis

Dive into the world of projectile motion to explore the interactions of vector and scalar quantities in curved paths. Learn how velocity vectors and vector addition play crucial roles in determining the flight path of objects through practical examples and explanations. Discover the impact of gravity and wind resistance on projectile motion, from launching projectiles vertically to understanding the ideal and actual paths of falling objects.

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Projectile Motion: Vector Quantity Analysis

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  1. Chapter 3PROJECTILE MOTION How does a cannonball fly?

  2. Or:Did you realize that gravity and wind resistance effect things ? • We’ve looked at LINEAR MOTION, or the motion of objects moving in a straight line. • Now we’ll look at NONLINEAR MOTION or motion along curved paths !

  3. When we throw a ball : • There is a constant velocity horizontal motion • And there is an accelerated vertical motion • These components actindependently of each other

  4. Vector and Scalar Quantities • Vector quantities require both magnitude and direction • They are represented by arrows with a numerical value amount attached. • EXAMPLES of Vector Quantities: Power velocity Force acceleration Electric Current directed energies

  5. Vector and Scalar Quantities • Scalar quantities require magnitude ONLY and have no direction component. • They are represented by a numerical value and units alone. • EXAMPLES of Scalar Quantities: Mass (grams) volume (ml, liters, cm3) time (sec., min., hr.) speed (m/sec) Scalars can be added, subtracted, multiplied or divided like ordinary numbers (3 kg + 4 kg = 7 kg) 15 min delay in a 60 min trip means the trip took 75 min.

  6. VELOCITY VECTORS • Represented by arrows. • The length of the arrow, drawn to scale, indicates the magnitude of the vector. • The direction of the arrow indicates the relative direction of the vector quantity. • Large quantity vector • Small quantity vector

  7. Velocity Vector EXAMPLE • An Airplane flying at 100 km/hr with a 20 km/hr wind • With the wind 100 km/hr + 20 km/hr = 120 km/hr • Against the wind • 100 km/hr - 20 km/hr = 80 km/hr

  8. So what happens when the plane meets a crosswind? • The resulting flight path is not straight, but IS a result of both velocity vectors. RESULTANT 20 km/hr crosswind 100 km/hr direction

  9. VECTOR ADDITION • 3 Step Technique • Finds the RESULTANTof a pair of component vectors that are at right angles (perpendicular) to each other. • 1. Draw the 2 vectors with their tails touching • 2. Draw a parallel projection of each vector to form a rectangle • 3. Draw the diagonal from the point where the 2 tails are touching

  10. VECTOR ADDITION – Step 1 • 3 • 4

  11. VECTOR ADDITION – Step 2 • 3 • 4

  12. VECTOR ADDITION – Step 3 • 3 • 5 • 37.50 4

  13. VECTOR ADDITION - Examples • Follow the example and complete the following vector addition exercises.

  14. Component Vectors • Sometimes vectors need to be changed into an equivalent set of Component vectors. • The vector is RESOLVED into 2 component vectors that are perpendicular to each other. • Any vector can be resolved into horizontal and vertical components.

  15. Components of Vectors • Resolving a vector into its components • Vertical Component Horizontal Component

  16. PROJECTILE MOTION • A falling object with constant linear velocity and vertical acceleration :

  17. Upwardly Launched Projectiles • Without gravity, a projectile launched upward would follow a straight line. • The vertical distance a projectile falls beneath any point on the dashed line is the same distance it would fall if dropped from rest! IDEAL PATH 45 m 20 m 5 m 2 sec 1 sec ACTUAL PATH 3 sec

  18. PROJECTILE MOTION • Launch a projectile from high enough and fast enough and it will fall around the curve of the Earth. • This is referred to as going into orbit and becoming a satellite.

  19. Velocity Vectors • An object is thrown in a long arc. • The horizontal vector does not change while the vertical vector changes due to gravity!

  20. Projectile Motion • End

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