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Remember: This Week & Upcoming Read Ch. 4.1‐4.6 on Newton’s Laws. Recita’on 3 this week : Print out RecitaDon Assignment and bring to recitaDon/lab secDon. CAPA assignment #5 is due Friday evening at 10 PM, to be done on‐line. L12 M 2/8/10 1 Physics 2010

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L12 M 2/8/10 Physics 2010 2 +y Vertical y-direction Horizontal x-direction θ v 0 v y ( t ) = v 0 sin θ− gt v x ( t ) = v 0 cos θ y ( t ) = y 0 + v 0 y t 1 2 gt 2 x ( t ) = v 0 x t v y 2 ( y ) = v y 0 2 2 g Δ y v x 2 ( x ) = v x 0 2 v x 0 v y 0 Kinematic Equations in 2D a y = g y 0 v 0 y = v 0 sin a x = 0 x 0 = 0 v 0 x = v 0 cos y 0 Kinematic equations for projectiles subject to gravity without air resistance.
L12 M 2/8/10 Physics 2010 3 t max = 2 v y 0 g = 2 v 0 sin θ g H = v y 0 2 2 g = v 0 2 sin 2 2 g R = 2 v x 0 v y 0 g = v 0 2 sin2 g H R You derived three formulas about the behavior of a projectile moving from ground level to ground level: Time of flight Height of apex “Range” – horizontal distance traveled. Summary: Ground to Ground Projectile 0 = x 0 = y 0

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L12 M 2/8/10 Physics 2010 4 R = 270 ft = 83 m θ =15° v 0 v 0 = 90 mi / h = 40 m / s H=5.5 m t max =2.1s (3) sin2 θ = Rg v 0 2 = (83)(9.9) (40) 2 = 0.51 = 15 (2) H = v 0 2 sin 2 2 g = 2 sin 2 15 19.6 m = 5.5 m (1) t max = 2 v 0 sin g = 2(40)(sin15 ) 9.8 s = 2.1 s t max = 2 v 0 sin g (2) H = v 0 2 sin 2 2 g (3) R = v 0 2 g Travis Pastrana, 2009
L12 M 2/8/10 Physics 2010 5 R = 1 mile = 1.6 km θ =45° v 0 v 0 ~ 250 mi / h ~120 m / s v 0 sin 45 ~ 85 m / s H?

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