physics help?

An astronaut drops a camera from rest while exiting a spacecraft on the Moon. The camera falls 2.3 m in 1.7 s. Calculate (a) the acceleration due to gravity on the Moon and (b) the impact velocity of the camera with the surface

4 Answers

Relevance
  • 1 month ago
    Favourite answer

    (a) From Newton's Universal Law of Gravitation: g = GM/r, where:

    *G = the gravitational constant, 6.67*10^-11 N*m^2/kg^2

    *M = the mass of the object = 7.35 * 10^22 kg

    *r = radius of the object = 1.74 * 10^6 m

    Plugging these values into the formula gives us g = 1.63 m/s^2

    Alternatively (and in retrospect probably more what you wanted) you can use kinematics:

    x = 1/2 * a * t^2 + v0 * t

    2.3 m = 1/2 * a * (1.7 s^2) + 0          (initial velocity is zero because it's from rest)

    a = 1.59 m/s^2

    The answers are slightly different, but I'm going to bet that's because of round-off error.

    (b) The distance dropped is very small compared to the radius, so acceleration can be assumed constant.

    v = v0 + a * t

    v = (0) + 1.59 m/s^2 * 1.7 s = 2.71 m/s

    Hope this helps!

  • oubaas
    Lv 7
    1 month ago

    2h = g*t^2

    g =2h/t^2 = 4.6/1.7^2 = 4.6/2.89 = 1.6 m/sec^2

    V = √ 2gh = √ 3.2+2.3 = 2.71 m/sec

  • 1 month ago

    (a) the acceleration due to gravity on the Moon

    d = distance through which the camera falls = 2.3 m

    t = elapsed time of the fall = 1.7 s

    a = gravitational acceleration on the Moon = to be determined

    t = √(2d / a)

    t² = 2d / a

    t²·a = 2d

    a = 2d / t²

    a = 2(2.3 m) / (1.7 s)²

    a = 1.591695502 ms² = 1.6 m/s²

    (b) the impact velocity of the camera with the surface

    vi = instantaneous velocity of an object after falling for t seconds = to be determined

    vi = a·t

    vi = 1.591696 m/s²·1.7 s

    vi = 2.705882353 m/s 2.7 m/s

  • a(t) = a

    v(t) = a * t + C

    v(0) = 0

    v(t) = a * t

    s(t) = (a/2) * t^2 + C

    s(0) = 2.3

    s(t) = (a/2) * t^2 + 2.3

    s(1.7) = 0

    0 = (a/2) * 1.7^2 + 2.3

    -2.3 = 2.89 * a / 2

    -4.6 = 2.89 * a

    a = -4.6 / 2.89

    a = -460 / 289

    v(1.7) = (-460/289) * 1.7 = (-460 / 17^2) * (17/10) = -46/17

Still have questions? Get answers by asking now.