1. Projectiles

2. Reading Assignment: (3.3) Projectile motion is a combination of A.Horizontal motion at constant acceleration and vertical motion at constant velocity B.Horizontal motion at constant velocity and vertical motion at constant acceleration C.Horizontal and vertical motion at constant velocity D.Horizontal and vertical motion at constant acceleration

3. Motion in 2d - Projectile Motion Coordinate system? x y x(t) y(t) Velocity? v(t) v x (t) v y (t) Acceleration? g Initial conditions? vivi  v ix v iy

4. How would that work? Consider a projectile that has been released with an initial velocity with a horizontal component of 10 m/s and a vertical component of 30 m/s. The initial position was 20m above the ground. For this problem, round g to 10 m/s 2. Time (s) 012345678 v x (m/s) v y (m/s) Time (s)12345678  x(m)  y(m) Example 13 page 2 10 m/s 30 m/s 10 m/s 20 m/s10 m/s0 m/s-10 m/s-20 m/s-30 m/s-40 m/s-50 m/s 10m 25m15m5m-5m-15m-25m-35m

5. Time (s)12345678  x(m)  y(m) 10m 25m15m5m-5m-15m-25m-35m x(m) y(m) 20 40 60 20406080

6. Parabolic trajectory 1. Eliminate time t to get y(x) 2. Use x- and y-components of initial velocity

7. Varying the initial angle Maximum range: 45°

8. Varying the initial speed

9. Varying the initial height

10. Example A projectile is shot from a height of 10 m at an angle of 30º with a muzzle speed of 20 m/s. –How far from the origin (horizontally) will the projectile land? –Which maximum height will the projectile reach? –With which speed does it impact the ground?

11. How fast was the driver going?

13. The date is January 27, 2009. A 23-year old missed a curve, raced up an incline, lost contact with the ground and ended up in the roof of the church. The location is a small town named Limbach- Oberfrohna in Saxony, Germany. The driver survived with injuries and is hospitalized. The impact point is located in a horizontal distance of 35 m and a vertical distance of 7 m away from the take-off point. The incline has an angle of approximately 25 o. Freie Presse, Jan 28, 2009 How fast was the driver going?

14. Question The hunter is aiming exactly at the monkey in the tree. The monkey releases its grip on the branch exactly when the gun is fired. The bullet will a.hit the monkey for any muzzle speed b.miss the monkey c.will hit the monkey only if the initial speed of the bullet is high

15. Monkey problem No gravity g With gravity