Lecture07_Motion_and_Curvature_9-2_3_mod

Lecture07_Motion_and_Curvature_9-2_3_mod - Engineering and...

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12 Engineering and Physics Examples ± Example : Centripetal Acceleration r of dierction opposite in the is a i.e., , ) ˆ sin ˆ cos ( ) ( ) ( ˆ cos ˆ sin ˆ sin ˆ cos 2 0 0 2 0 0 0 0 r r r r r r r r j i r a j i j i r ω = + = = + = + = t r t r t t t r t r v t r t r 0 2 / || || ||, || with r v a v a = = = v a
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15 Engineering and Physics Examples ± Example (P9.2-17) Projectile A projectile is fired from a cannon directly at a target that is dropped from rest simultaneously as the canon is fired. Show that the projectile will strike the target midair. (0,0) (x o ,y o ) r p r T
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16 ± Example (Cont.) (0,0) (x o ,y o ) P T θ
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17 Example (Cont.) With is At that time, the vertical component of r p (t) is (x o ,y o ) P T θ which equals to the vertical component of r t (t).
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18 Important Remark Or, Time rate of distance= speed ? || || say can we , v v r = = = v dt ds dt d Yes v t dt ds s du u r dt t r s dt ds ds d dt d s b a = = = = = = || ) ( || 1
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Lecture07_Motion_and_Curvature_9-2_3_mod - Engineering and...

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