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Unformatted text preview: Review • Projectiles • Relative velocity • Newtons laws • Motion in a circle • Energy • Momentum • Rotational motion • Statics Lecture 4 in a nutshell ( 29 1 x x υ υ = x → ( 29 2 x x t υ ∆ = y → ( 29 1 y y gt υ υ = ( 29 2 1 2 2 y y t gt υ ∆ = ( 29 2 2 2 3 y y g y υ υ = ∆ ( 29 4 2 y y y t υ υ + ∆ = Motion in the vertical and horizontal directions are independent. However t is common Equations in both dimensions are necessary to solve most problems. Projectile motion: maximum height and time of flight y t υ 2 2 gt y y y = ∆ = y ∆ A baseball player tries to hit a ‘home run’. If the ball had initial height of 1m off of the ground and the boundary is 150m away and has a height of 3m how high above the boundary does the ball travel if the initial velocity of the ball was 100 m/s and the angle to the horizontal was 30°?. What is the velocity as the ball passes the boundary? 150 x ∆ = 1 y = ( 29 2 1 2 2 x t at υ ∆ = + ( 29 2 2 2 3 a x υ υ = + ∆ ( 29 4 2 x t υ υ + ∆ = ( 29 1 at υ υ = + θ υ y υ x υ ( 29 cos υ θ = ( 29 sin υ θ = Remember t is common 3 h m = ? t = υ θ ? y ∆ = υ r θ x υ y υ x ∆ ? t = ( 29 2 x x t υ ∆ = x x t υ ∆ = ( 29 ( 29 ( 29 ( 29 2 1 sin cos 2 cos x x y g υ θ υ θ υ θ ∆ ∆ ∆ = ÷ ÷ ÷ ÷ Projectile motion: maximum height and time of flight y ∆ A baseball player tries to hit a ‘home run’. If the ball had initial height of 1m off of the ground and the boundary is 150m away and has a height of 3m how high above the boundary does the ball travel if the initial velocity of the ball was 100 m/s and the angle to the horizontal was 30°?. What is the velocity as the ball passes the boundary? 150 x ∆ = 1 y = ( 29 2 1 2 2 x t at υ ∆ = + ( 29 2 2 2 3 a x υ υ = + ∆ ( 29 4 2 x t υ υ + ∆ = ( 29 1 at υ υ = + 3 h m = ( 29 ( 29 ( 29 ( 29 2 150 1 150 sin 30 9.8 cos 30 2 100cos 30 y ∆ = ÷ ÷ ÷ ÷ 71.9 72 m = ≈ 1 ha h y + = + ∆ ha 1 ha y h = + ∆  1 72 3 70 ha m = + = y ∆ A baseball player tries to hit a ‘home run’. If the ball had initial height of 1m off of the ground and the boundary is 150m away and has a height of 3m how high above the boundary does the ball travel if the initial velocity of the ball was 100 m/s and the angle to the horizontal was 30°?. What is the velocity as the ball passes the boundary? 150 x ∆ = 1 y = ( 29 2 1 2 2 x t at υ ∆ = + ( 29 2 2 2 3 a x υ υ = + ∆ ( 29 4 2 x t υ υ + ∆ = ( 29 1 at υ υ = + 72 y ∆ = υ r θ x υ y υ x ∆ t θ υ y υ x υ 2 2 x y υ υ υ = + r ( 29 2 2 2 xo y g y υ υ = + ∆ ( 29 ( 29 ( 29 ( 29 ( 29 2 2 cos sin 2 g y υ υ θ υ θ = + ∆ ( 29 ( 29 ( 29 ( 29 ( 29 2 2 100cos 30 100sin 30 2 9.8 72 υ = + × × ( 29 7500 2500 1411 υ = + 92.7 / m s = Projectile motion: example problems y ∆ A baseball player tries to hit a ‘home run’. If the ball had initial height A baseball player tries to hit a ‘home run’....
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 Fall '07
 Dr.Jackman
 Physics, Angular Momentum, Energy, Force, Mass, Momentum, θ

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