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12 October, 16:20

A toy rocket, launched from the ground, rises vertically with an acceleration of 20 m/s2 for 6.0 s until its motor stops. Disregarding any air resistance, what maximum height above the ground will the rocket achieve?

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  1. 12 October, 18:43
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    h = 1094.69m

    The maximum height above the ground the rocket will achieve is 1094.69m.

    Explanation:

    The maximum height h is;

    h = height covered during acceleration plus height covered when the motor stops.

    h = h1 + h2 ... 1

    height covered during acceleration h1 can be derived using the equation of motion;

    h1 = ut + 0.5at^2

    Initial speed u = 0

    h1 = 0.5at^2

    acceleration a = 20 m/s^2

    Time t = 6.0 s

    h1 = 0.5 * (20 * 6^2)

    h1 = 0.5 (20*36)

    h1 = 360 m

    height covered when the motor stops h2 can be derived using equation of motion;

    h2 = ut + 0.5at^2 ... 2

    Where;

    a = g = acceleration due to gravity = - 9.8 m/s^2

    The speed when the motor stops u;

    u = at = 20 m/s^2 * 6.0 s = 120 m/s

    Time t2 can be derived from;

    v = u - gt

    v = 0 (at maximum height velocity is zero)

    u = gt

    t = u/g

    t = 120m/s / 9.8m/s^2

    t = 12.24 seconds.

    Substituting the values into equation 2;

    h2 = 120 (12.24) - 0.5 (9.8*12.24^2)

    h2 = 734.69376 m

    h2 = 734.69 m

    From equation 1;

    h = h1 + h2. substituting the values;

    h = 360m + 734.69m

    h = 1094.69m

    The maximum height above the ground the rocket will achieve is 1094.69m.
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