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28 June, 12:06

problem A newly established colony on the Moon launches a capsule vertically with an initial speed of 1.445 km/s. Ignoring the rotation of the Moon, what is the maximum height reached by the capsule

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  1. 28 June, 13:41
    0
    Maximum height = 1031km

    Explanation:

    Given:

    Velocity, Vo = 1.445km/s = 1445m/s

    Mass of moon = 7.35*10^22kg

    Radius of moon = 1737km = 1737000m

    Using conservation energy

    Ui + Ki = Uf + Kf

    --'> (GMm/R) + 1/2 (m ^2)

    -GMm / (R + h) - 0

    Vo^2 = 2Gm (1/R - 1/R+h)

    1445^2 = 2 * (6.67x10^-11) * (7.35*10^22) [ (1/1737000) - (1/1737000 + h) ]

    h = 1031km
  2. 28 June, 15:30
    0
    104.4km

    Explanation:

    Projectile motion occurs when object is launched into air and allowed to fall freely under the influence of gravity.

    Maximum height reached by the object is expressed as;

    H = u²sin² (theta) / 2g where;

    u is the initial velocity = 1.445km/s

    u = 1445m/s since 1000m is equivalent to 1km

    theta is the angle of launch

    g is the acceleration due to gravity = 10m/s²

    theta = 90° (since object is launched vertically)

    Substituting the values in the formula we have;

    H = 1445² (sin90°) ²/2 (10)

    H = 1445²/20

    H = 104,401.25m

    H = 104.4km

    The the maximum height reached by the capsule is 104.4km
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