1. HUMP DAAAAY! More projectile motion… with angles! Make sure your calculators are in degrees NOT radians HW: WebAssign and POTW

2. Warm-Up A Wile E Coyote runs horizontally off a high cliff at a speed of 25 m/s. He hits the canyon floor below 5.8 seconds later. How high is the cliff? How far out from the cliff edge does he land in the canyon below? What are his horizontal and vertical velocities at impact?

3. Only Horizontal? So far we have seen problems where the initial velocity is horizontal. Not always realistic, right? Let’s look at angular projectile motion, it’s much more fun. Equations are the same but we must use what we just learned about vectors to find the horizontal and vertical parts of the velocity.

4. Vectors Scalars are easy: add/subtract just like everyday numbers. –2 kg + 3kg = 5kg Vectors are more complicated: –2 + 3 could equal 4 The classic way to add vectors is to represent them as arrows. –Draw them to scale –Measure out things with a ruler and protractor and see what the answer would be. You should be able to do a rough sketch but this process isn’t necessarily all that useful.

5. Vectors and Trigonometry

6. Vector Components Any vector can be drawn as the resultant of two perpendicular vectors: –One along the horizontal (x) axis –One along the vertical (y) axis Using the trig. Functions (or Pythagoreans theorem) any of the “sides” and the angle can be found. A AxAx AyAy θ A AxAx AyAy θ

7. Sample A projectile is launched at an angle of 50 degrees above the horizontal at 15 m/s. Determine the horizontal and vertical components of the velocity.

8. Sample A velocity vector has the following components: v y is 12.4 m/s and v x is 15.4 m/s, find the resultant velocity and angle θ of launch.

9. Sample A boat is traveling north directly across a river that is 5.0 km across. The current is to the east at 3.0 km/h. The boat travels at 5.0 km/h. (a)What is the boat’s resultant velocity? (b)How long does it take to cross the river? (c)How far down the bank does it drift before it reaches the far side?

10. Sample A quarterback throws a ball at 15 m/sec at an angle of 30 o above the horizontal. How far will the ball travel if it caught by a wide receiver at the same height it was released?

11. Sample During a fireworks display, a shell is shot into the air with an initial speed of 70.0 m/s at an angle of 75.0º above the horizontal. The fuse is timed to ignite the shell just as it reaches its highest point above the ground. a)Calculate the height at which the shell explodes. b)How much time passed between the launch of the shell and the explosion? c)What is the horizontal displacement of the shell when it explodes?

12. Sample – Maximum Range

13. Problem #6