PH 211 Fall 2007 Midterm 1 Workout_Problem_1

PH 211 Fall 2007 Midterm 1 Workout_Problem_1 - Show Work...

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Show Work Problem #1 a) To find the initial velocity for ball 2 we use one of kinematics equations. 2 1 2 8 . 9 s m a a x x - = = , s m v v i f 0 1 2 = = , m x x f i 0 1 2 = = , m x x i f 10 1 2 = = ( 29 x a v v x i f + = 2 2 2 2 2 2 ( 29 x a v x i + = 2 2 2 2 0 ( 29 x a v x i - = 2 2 2 2 ( 29 s m m m s m v i 0 . 14 0 10 8 . 9 2 2 2 = - - - = b) We can find the time that it takes for the balls to pass each other two ways. Way 1 We can use a kinematics equation for ball 1 and ball 2. Also we will note that when the balls pass each other their positions are equal, m m x x 2 1 = , and the time will be the same, m m t t 2 1 = . Ball 1: 2 1 1 1 1 2 1 m x m i i m t a t v x x + + = 2 1 1 1 2 1 0 m x i m t a x x + + = Ball 2: 2 2 2 2 2 2 1 m x m i i m t a t v x x + + = 2 2 2 2 2 1 0 m x m i m t a t v x + + = Since m m x x 2 1 = , we can set the two equations equal.
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= = + m m x i x t a x 1 2 1 1 2 1 2 2 2 2 2 1 m x m i m t a t v x + = 2 2 2 2 1 1 2 1 2 1 m x m i m x i t a t v t a x + = + 2 2 2 2 1 1 2 1 2 1 m x m i m x i t a t v t a x + + - = 0 2 1 + = m i i t v x s s s m m v x t i i m 714 . 0
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