Ex_2Dmotion_xy

Ex_2Dmotion_xy - 2-D Particle Kinematics Motion in x-y...

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2-D Particle Kinematics – Motion in x-y coordinates Position: Vector definition – position vector 22 ˆˆ () () , tan / rt xti yt j r x y y x θ =+ = + = G Velocity: average velocity 21 ave rr r ttt υ Δ == Δ G G G G , instantaneous velocity , / xy x yx y dr ij dt dx dy dt dt υυ y x α ==+ ⇒= = = + = G G Acceleration: average acceleration ave a tt t Δ Δ G G G G , instantaneous acceleration 2 2 / y x x y dd r aa i a j dt dt d d dx dy a a a dt dt dt dt β ⇒= = = = = + = G y x a a G G Projectile motion Horizontal: 00 0 0 cos (c o s) x x a x xt υυ α = = Vertical: 2 0 sin 1 (s i n ) 2 i n ) 2 ( ) y y y ag gt 0 y yt g t g yy υα υυα =− Example 1. A football kicker attempts a 40 m field goal. The football leaves the ground with an initial speed 0 at a 50 ° angle with the horizontal. Knowing that the height of the crossbar is 3.05 m, calculate the minimum value of the initial speed 0 for the kicker to make the field goal. ( Ans : 20.6 m/s)
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2. The pilot of the airplane has to release a package to hit the target at A . The plane is flying horizontally at an altitude of 640 m with a constant speed of
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Ex_2Dmotion_xy - 2-D Particle Kinematics Motion in x-y...

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