Physics 1710 Chapter 4: 2-D Motion—I

1. 0 Physics 1710 Chapter 4: 2-D Motion—I Demonstration: Stuntman Lead REVIEW

2. t = √(2h/g) d = vtruck t 0 Physics 1710 Chapter 4: 2-D Motion—I No lead Demonstration: Stuntman Lead REVIEW

3. t = √(2h/g) d = vtruck t 0 Physics 1710 Chapter 4: 2-D Motion—I Proper lead d = vtruck√(2h/g) d =(15 m/s)√[2 (3.15 m)/9.8 m/s2)] d= 12.0 m Demonstration: Stuntman Lead REVIEW

4. 0 Physics 1710 Chapter 4: 2-D Motion—I 1′ Lecture Displacement, velocity and acceleration are vector quantities in two or more dimensions. Each component of the kinematic variables isseparateandindependent. In projectile motion the x-motion is unaccelerated while the y-motion experiences a constant acceleration equal to -g.

5. 0 Physics 1710 Chapter 4: 2-D Motion—I Position r is a vector. r= x i + y j Or rx = x & ry = y Thus, one can represent a vector by a position vector, ie an arrow.

6. 0 Physics 1710 Chapter 4: 2-D Motion—I Displacement in 2-D is a vector ∆ r = rfinal - rinitial [∆ r]x=xfinal - xinitial = ∆x [∆ r]y=yfinal - yinitial = ∆y ∆ r = ⃓∆ r⃓ ⃓∆ r⃓ =√(x final - x initial ) 2+ (yfinal - yinitial) 2 Tan θ = (yfinal - yinitial)/ (x final - x initial )

7. 0 Physics 1710 Chapter 4: 2-D Motion—I y(x) = trajectory y(t) Average velocity is a vector : vave≡ ∆ r / ∆t This means the following: vx, ave ≡ ∆ x / ∆t ; vy, ave ≡ ∆ y / ∆t . y x x(t) t

8. 0 Physics 1710 Chapter 4: 2-D Motion—I vy, ave ≡ ∆ y / ∆t y(x) = trajectory y(t) Average velocity is a vector : y x x(t) vx, ave ≡ ∆ x / ∆t t

9. 0 Physics 1710 Chapter 4: 2-D Motion—I Instantaneous velocity is a vector : v ≡ lim ∆t → 0∆ r / ∆t This means the following: vx ≡ lim ∆t → 0 ∆ x / ∆t = dx /dt vy ≡ lim ∆t → 0∆ y / ∆t = dy/dt

10. vy≡ dy /dt vx≡ dx /dt 0 Physics 1710 Chapter 4: 2-D Motion—I Instantaneous velocity is a vector : y x t

11. 0 Physics 1710 Chapter 4: 2-D Motion—I Average acceleration is a vector : aave≡ ∆ v / ∆t This means the following: ax, ave ≡ ∆vx / ∆t ; ay, ave ≡ ∆vy / ∆t .

12. 0 Physics 1710 Chapter 4: 2-D Motion—I Instantaneous acceleration is a vector : a ≡ lim ∆t → 0∆ v / ∆t This means the following: ax ≡ lim ∆t → 0 ∆ vx / ∆t = dvx /dt ay ≡ lim ∆t → 0∆ vy / ∆t = dvy /dt N.B.: The components are strictly segregated!

13. 0 Physics 1710 Chapter 4: 2-D Motion—I Motion in Two Dimensions All the one dimensional kinematic equations can be generalized to two (or more) dimensions. All the component equations obey the one dimensional kinematics separately.

14. No Talking! Think! Confer! 0 Physics 1710 Chapter 4: 3-D Motion—I Two two balls are simultaneously shot horizontally and dropped,which will the ground first? Why? REVIEW

15. 0 Physics 1710 Chapter 4: 2-D Motion—I Vector kinematic equations (uniform a): rfinal= rinitial + vinitialt + ½ a t 2 vfinal=vinitial + a t

16. 0 Physics 1710 Chapter 4: 2-D Motion—I Projectile Motion: Horizontal acceleration: ax =0 ∴ vx, final = vx, initial ; xfinal = x initial+ vx, initial t . Vertical acceleration: ay = -g ∴ vy, final = vy, initial - g t ; yfinal = y initial+ vy, initial t - ½ g t 2

17. 0 Physics 1710 Chapter 4: 2-D Motion—II Summary: Kinematics in two (or more) dimensions obeys the same 1- D equations in each component independently. rfinal= rinitial + vinitialt + ½ a t 2 vfinal=vinitial + a t vx,final2 = vx,initial2+ 2 ax /∆x vy,final2 = vy,initial2+ 2 ay /∆y Projectiles follow a parabola [y(x) = A + Bx +Cx2]