2 displacement vectors y Displacement Vector: A B △r=r Cautio B △r|=AB △f≠AB △s=AB Displacement is different from distance
2) displacement vectors r B r B A A r O x y Displacement Vector: r B A r r r = − r = AB Cautio n! r AB s = AB Displacement is different from distance
Discussion: A very small displacement during a small time interval A very small displacement: dr= AB A very small distance: ds B ds= AB When time interval rde dr approaches to 0 dr=ds B Let: 0A=OC Acre CB= dr AB=AC+cB Cautio d≠d dr= ac+cb=rde+drr
Discussion: A very small displacement during a small time interval O y A r B r B A x dr ds ds = AB dr = ds When time interval approaches to 0: dr = AB A very small displacement: A very small distance: C dr AC = rd drr ˆ ˆ dr = AC +CB = rd + Let: OA= OC AB = AC +CB d rd CB = dr Cautio n! dr dr
Airplane 790m 123° 360m 40° Radar dish EXample: a radar station detects an airplane approaching directly from the east. At first observation, the range to plane is 360m at 400 above the horizon. The plane is tracked for another 1230 in the vertical east-west plane, the range at final contact being 790m Find displacement of the airplanes during the period of observation
Example: a radar station detects an airplane approaching directly from the east. At first observation, the range to plane is 360m at 400 above the horizon. The plane is tracked for another 1230 in the vertical east-west plane, the range at final contact being 790m. Find displacement of the airplanes during the period of observation
Airplane 790m 123° 360m 40 Radar dish Solution: 901851+21
Solution:
3)Motional equation r=xi +yj+zk Motional P=r(t=x(t)i+y(tj+z(t k equation x=x(t),y=y(t),=z(t) Examplet=6cos 2t Path y=sin 2t equation Path graph 2v2=2
3) Motional equation Motional equation x = x(t), y = y(t),z = z(t) r r t x t i y t j z t k ˆ ( ) ˆ ( ) ˆ = ( ) = ( ) + + x 2+y2=62 x y Path equation Path graph r xi yj zk ˆ ˆ ˆ = + + = = y t x t 6sin2 6cos 2 Example: