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Ballistic_Motion_0212_handout

# Ballistic_Motion_0212_handout - Ballistic Motion h1 =...

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cceleration in One Dimension PHYS 0212 BallisticMotion 1 Bench Top Ballistic Launcher Impact Point Start Point Launch Point Plumb Bob A 1 h 2 h Impact Distance h 1 = Height of the center of mass above the launch point h 2 = Height of the launch point above the table Ballistic Motion PHYS 0212 BallisticMotion 2 The basic procedure: 3. Measure the impact distance as a function of height h 2 . 1. Repeatedly measure the impact distance for a fixed height h 2 . A 2. Calculate the mean and standard deviation of the impact distance . A 4. Plot versus h 2 . 2 A We can find the impact distance of the ball if we know its velocity at the launch point. Horizontal ( x ) and vertical ( y ) motions are independent, so we can write out the equations of motion for constant acceleration. x -direction y -direction 2 1 0 0 2 x x x x v t a t = + + 2 1 0 0 2 y y y y v t a t = + + 0 0 0 0 0 x x x v v a = = = 0 2 0 0 y y y h a g v = = = − At the launch point ( assuming the initial velocity is completely horizontal ) } { PHYS 0212 BallisticMotion 3 x -direction y -direction ( ) ( ) 2 1 0 0 2 2 1 0 2 0 0 x x x x v t a t x v t t = + + = + + ( ) ( ) 2 1 0 0 2 2 1 2 2 0 y y y y v t a t y h t g t = + + = + + 0 x v t = 2 1 2 2 y h gt = Bench Top A Impact Distance 2 h When the ball reaches the impact point: and 0 x y = = A 0 v t = A 2 1 2 2 0 h gt = The time t is the same in both of these equations. 0 v PHYS 0212 BallisticMotion 4 0 2 2 2 0 t v t v = = A A 2 1 2 2 2 0 h g v = A 0 v t = A 2 1 2 2 0 h gt = Eliminate t from both equations: 2 2 2 0 2 h v g = A Solve for 2 A 2 1 2 2 h gt =

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