Motion_and_Curvature9-2&3

Solution r gravitional acceleration a g j 0 v adt

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Unformatted text preview: tˆ + ⎢− gt 2 + (v0 sin θ )t ⎥ ˆ + c2 i j ⎣2 ⎦ r j Q r ( 0) = s j ⇒ c = s ˆ Find the speed and position at any time instant t. Solution: r Gravitional acceleration : a = − gˆ j 0 v = ∫ adt , r (t ) = ∫ vdt r r v(t ) = ∫ (− gˆ)dt = − gtˆ + c1 j j 2 0 ⎡1 ⎤ ∴ r (t ) = (v0 cos θ )ti + ⎢− gt 2 + (v0 sin θ )t + s0 ⎥ j ⎣2 ⎦ Since v (0) = v0 cos θ i + v0 sin θ j. x(t ) = (v0 cos θ)t , r ⇒ c1 = (v0 cos θ )ˆ + (v0 sin θ )ˆ i j 13 1 y (t ) = − gt 2 + (v0 sin θ)t + s0 2 14 Example (Cont.) 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. T P (xo ,yo) θ (0,0) (xo ,yo) (0,0) 15 16 4 1/2/2011 Example (Cont.) Important Remark (xo ,yo) T P dr ds = v, can we say = v =|| v || ? dt dt θ Yes b s dr dr ds = , s = ∫ || r (t ) || dt = ∫ || r ′(u ) || du || a 0 dt ds dt ds ⇒ || r′( s ) ||= 1 ⇒ =|| r...
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This note was uploaded on 06/30/2011 for the course ENGR 233 taught by Professor S.samuelli during the Winter '10 term at Concordia Canada.

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