Ex_2Dmotion_xy

Ex_2Dmotion_xy - 2-D Motion in x-y coordinates ^ Position:...

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2-D 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: 21 ave rr r ttt υ Δ == Δ− GG G G , , / x yx y x y y d r dx dy ij dt dt dt x υυ υυυ α ==+⇒ = = = + = G G Acceleration: ave a tt t Δ G G , 2 2 / y x x y x y y d d dd r d x d y aa i a j a a a a a dt dt dt dt dt dt β =+⇒ = = = = = + = G G G x a a Projectile motion 00 0 2 0 0 Horizontal: 0, cos , ( cos ) 1 Vertical: sin , ( sin ) , ( sin ) 2 ( ) 2 xx yy y ax x t ag g t y y t g t g y y υυ α υ α υ υ α = + =− = = + = 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 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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