Ballistic_Motion_0212_handout

Ballistic_Motion_0212_handout - Ballistic Motion h1 =...

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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 00 2 xx xxv t a t =+ + 2 1 2 yy y yv t 0 0 0 0 0 x x x vv a = = = 02 0 0 y y y h ag v = = = − At the launch point ( assuming the initial velocity is completely horizontal ) }{ PHYS 0212 BallisticMotion 3 x -direction y -direction () 2 1 2 2 1 0 2 t x vt t =+ + 2 1 2 2 1 2 2 0 yyv t y htg t =+ +− 0 x = 2 1 2 2 y hg t =− Bench Top A Impact Distance 2 h When the ball reaches the impact point: and 0 xy == A 0 = A 2 1 2 2 0 t 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 v  =   A 0 = A 2 1 2 2 0 t Eliminate t from both equations: 22 2 0 2 h v g = A Solve for 2 A 2 1 2 2 t = Okay, so how do we determine the initial velocity v 0 ?
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Ballistic_Motion_0212_handout - Ballistic Motion h1 =...

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