Projectile Motion: Vectors

Transcription

1 Projectile Motion: Vectors Ch. 5 in your text book Students will be able to: 1) Add smaller vectors going in the same direction to get one large vector for that direction 2) Draw a resultant vector for a given vertical and horizontal vector 3) Calculate the magnitude of a resultant vector based on the magnitudes of the horizontal and vertical vectors 4) Draw the direction of velocity vector for a projectile motion object

2 Vector Review Vectors have a magnitude and a direction. They are represented by an arrow.

3 Vector Addition The magnitudes of all vectors pointing in the same directions can be added, just as numbers. The end of one vector can be put on the tip of the previous (tip to tail). 1m 1m 1m 1m 4m =

4 Vector Addition Longer vectors mean larger magnitudes, smaller vectors mean smaller magnitudes. The vectors don t have to be next to each other in order to add them, they just have to be going in the same direction. 1m 1m 1m 1m 1m = 3m 2m

5 Vector Addition Check for understanding: Add the vectors below 1m 1m 2m 1m = There is more than one correct way to add vectors. In the end, it is all the same. Regardless of the path, you end up in the same place.

6 Vector Addition Look at your map. Regardless of the path, you end up in the same place. What path would you take if you were to fly to your destination? Vectors aren t always horizontal or vertical; they can be at angles too. =

7 Resultant Vectors How would you add these two vectors? You can add them, and it s just like how you drew a direct path from school to your final location on the map. This type of vector is called a resultant vector.

8 Vector Addition Remember these vectors? What would the resultant vector look like? = We will not be doing lots of vectors like this, but you will see them in later classes if you continue with math and science.

9 Resultant Vectors How would you calculate the magnitude of the resultant vector? 3m 2m a 2 + b 2 = c 2 (3) 2 + (2) 2 = c 2 c = 13 = 3.61 m Why do we care about any of this vector stuff? Velocity is a vector.

10 Vector Components When something is thrown or shot, it has a velocity. That velocity is a vector and it is most likely at an angle to the ground. The vector is a resultant vector. The horizontal and vertical vectors that add to that resultant are called components. There is a horizontal velocity component and a vertical velocity component. θ v v H v v

11 What does component mean? Vector Components Component = a part/portion of something larger Example A screen is one component of a phone With your partner, come up with a list of three components for different things. I ll call on some of you to give your examples in a minute

12 Vector Components v The actual velocity of the object; the resultant vector v H The horizontal component of the velocity. This is how fast the object is moving horizontally. v v The vertical component of the velocity. This is how fast the object is moving vertically. θ v v H v v

13 Vector Components For projectile motion, horizontal and vertical motion must be treated independently of each other; neither affect what happens to the other. Example:

14 Vectors For Flying Objects The velocity vector shows the direction of the object s velocity. As we ve discussed, if it s moving at a constant velocity, the vector won t change, but if the velocity is changing, the arrow will too.

15 Vectors For Flying Objects The ball in the video was moving in two directions at once. Each direction is a component to its velocity. Lets look at them.

16 Vectors For Flying Objects Look at just the horizontal arrows. What do you notice? No Δv = no acceleration. What is our equation for a constant velocity? x = v H t This equation will be used for questions involving horizontal motion.

17 Vectors For Flying Objects Look at just the vertical arrows. What do you notice? Δv = acceleration. What is causing the acceleration? x = v v t +.5at 2 This equation will be used for questions involving vertical motion.

18 Vectors For Flying Objects What about the acceleration vector? Which way is it pointing? Acceleration will always be pointing down. That is why the trajectory looks like an upside down parabola (y = -x 2 )

19 Horizontal Separate From Vertical The horizontal and vertical motions do not influence each other. Example: Say there are two, identical steel balls, that start at the same height and begin to fall at the same time. If one is dropped and the rolled off a ramp, which will hit the ground first? 1 2 Let s go try it

20 Horizontal Separate From Vertical All objects fall at the same rate. We also know that horizontal and vertical motions do not influence each other. If you look at just the vertical motion, there is no difference between the two spheres, so they land at the same time.

21 Horizontal Separate From Vertical Example: If a bullet was shot horizontally, and at the same time another was dropped from the same height, which would hit the ground first?

22 Direction of Velocity Check for understanding: For the three scenarios below, draw the direction of the velocity vector when the ball is: a) Rolling off a desk b) Rolling off a ramp upward c) Rolling off a ramp down

23 Direction of Velocity Check for understanding: For the three scenarios below, draw the horizontal and vertical components for each velocity vector a) Rolling off a desk b) Rolling off a ramp upward c) Rolling off a ramp down