2-D Motion in x-ycoordinates •Position: Vector definition – position vector 22ˆˆ()() , tan/rtxti yt j rxyy xθ=+=+=G•Velocity: 21averrrtttυ−Δ==Δ−GGGG, , /xyxyxyyd rdxdyijdtdtdtxυυυυυα==+⇒===+=GG•Acceleration: aveattt−ΔGG, 22/yxxyxyyddddrdxdyaaiajaaaaadtdtdtdtdtdtβ=+⇒=====+=GGGxaa−Projectile motion 000200Horizontal: 0, cos, (cos)1Vertical: sin, (sin), (sin)2 ()2xxyyyaxxtaggtyytgtgyyυυ αυ αυ υ α=+=−=−=+−=−−Example 1. A football kicker attempts a 40 m field goal. The football leaves the ground with an initial speed 0at 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 0for 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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