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Quiz_1_solutions_web - Quiz 1 Question 1 A 4th July rocket...

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Quiz 1 Question 1 A 4 th July rocket accelerates from rest uniformly and vertically up from the ground. After 5 seconds the rocket’s stick drops off and moves independently, hitting the ground 6 seconds later. What was the acceleration of the rocket? How high was the rocket when the stick fell off? Take g=9.8m/s 2 and ignore air resistance. We will use the physics of linear motion with constant acceleration Choose a coordinate system with y=0 at the ground and y increasing upwards Initial conditions for the rocket are y 0r =0, v 0r =0. The position of the rocket (y r ) after time t is given by y r =y 0r +v 0r t+1/2at 2 =1/2at 2 The velocity of the rocket is v r =v 0r +at At the time t 1 when the stick falls off y r1 =1/2at 1 2 v r1 =at 1 The stick now falls under gravity, its position y s time t after falling off is given by y s = y s1 +v s1 t-1/2gt 2 At the point where the stick falls off y s1 =y r1 , v s1 =v r1 When the stick hits the ground after time t 2 , y s =0 0=1/2at 1 2 +at 1 t 2 -1/2gt 2 2 We know everything except a a(1/2t 1 2 +t 1 t 2 )=1/2gt 2 2 2 2 2 0.5 9.8 6 176.4 4.2 / (0.5 5 5 6) 42.5 am s ×× == = ×+× The height of the rocket was y r1 =1/2at 1 2 =0.5x4.15x25= 52.0m Both results to 2 significant figures Check for reasonableness? Acceleration is 0.5g, OK, height is typical rocket height, OK
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Quiz_1_solutions_web - Quiz 1 Question 1 A 4th July rocket...

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