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Math Help - Another Kinematics problem

  1. #1
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    Another Kinematics problem

    A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the side of the rocket. The bolt hits the ground 6.60 later.

    What is the rocket's acceleration?



    I'm wanting to use the 3 kinematics equations but I feel like i'm missing information. I know what the answer is already but I want to understand how to get it. It seems I can't simply use the equations for 1D kinematics so if anyone can show me i'd be much obliged.
    Last edited by JonathanEyoon; January 19th 2009 at 08:00 AM.
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  2. #2
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    A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the side of the rocket. The bolt hits the ground 6.60 later.

    What is the rocket's acceleration?


    Let accln. of the rocket=a

    velocity of Bolt= velocity of rocket after 4 sec.= 4a .............upwards.................first eq of kinematics...


    dist. covered by rocket in 4 sec.= 1/2 XaX 4X4= 8a ................................second eq of kinematics


    now the Bolt falls from this height(8a) with accln. due to gravity in 6.6sec.

    second eq of kinematics

    s=ut-1/2 g t^2 .............................free fall
    8a= 4a-1/2 X (9.8 X6.6X6.6)
    solve this......
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  3. #3
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    while the bolt rides with the rocket (assuming the rocket started from rest) ...

    v = 4a

    \Delta y = \frac{(4a)^2 - 0^2}{2a} = 8a

    when the bolt gets free, a = -g ...

    \Delta y = 4a \cdot t - \frac{1}{2}gt^2

    -8a = 4a(6.6) - \frac{1}{2}g(6.6)^2

    -34.4a = - \frac{1}{2}g(6.6)^2

    a = \frac{g(6.6)^2}{2(34.4)} \approx 6.2 \, m/s^2
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  4. #4
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    Quote Originally Posted by JonathanEyoon View Post
    A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the side of the rocket. The bolt hits the ground 6.60 later.

    What is the rocket's acceleration?



    I'm wanting to use the 3 kinematics equations but I feel like i'm missing information. I know what the answer is already but I want to understand how to get it. It seems I can't simply use the equations for 1D kinematics so if anyone can show me i'd be much obliged.
    Split the problem into two parts! Part 1 and part 2!

    In part 1, the bolt is being accelerated from rest for 4 seconds.

     v_1 = u_1 + a_1t_1

     v_1 =  a_1t_1

     v_1 =  4a_1

    We don't know what value of the acceleration, that's what we're trying to find! But we do know one thing about it, it's negative, since the rocket flies upwards.

    Now let's have a look at part 2. In part 2 the bolt has a negative velocity  v_1 = 4a_1 , and it accelerates towards the ground with  a_2 = 9.81 ms^{-2} . And it then hits the ground and has velocity 0, and this process takes 6.6 seconds!

     v_2 = u_2 + a_2t_2

     0 = 4a_1 + 9.81(6.6)

    How's that?
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  5. #5
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    you guys are the best. I appreciate it!!!
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