I mean for the distance from the former question ☝️

Mathematics

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Answer

31.6 m\text{31.6 m}

Step-by-step solution

3 steps

You are asking to use the general kinematic equation S=ut+12at2S = ut + \frac{1}{2}at^2 to solve for the horizontal distance, which was denoted as RR in the previous problem (and you are referring to as 'c').

  1. Apply the kinematic equation to horizontal motion.

    For horizontal motion, the displacement SS becomes the horizontal distance RR, the initial velocity uu becomes the initial horizontal velocity uxu_x, and the acceleration aa becomes the horizontal acceleration axa_x.

    R=uxt+12axt2R = u_x t + \frac{1}{2}a_x t^2
  2. Substitute the value for horizontal acceleration.

    In projectile motion, assuming no air resistance, the horizontal acceleration axa_x is 0 m/s20 \, \text{m/s}^2.

    R=uxt+12(0)t2R = u_x t + \frac{1}{2}(0)t^2 R=uxtR = u_x t
  3. Substitute the values from the previous problem.

    From the previous problem:
    Initial horizontal velocity ux=10 m/su_x = 10 \, \text{m/s}
    Time taken to reach the ground t=10 st = \sqrt{10} \, \text{s} (calculated in part a)

    R=(10 m/s)(10 s)R = (10 \, \text{m/s})(\sqrt{10} \, \text{s}) R=1010 mR = 10\sqrt{10} \, \text{m} R≈31.62 mR \approx 31.62 \, \text{m}

    The horizontal distance (c) is 31.6 m\text{31.6 m}.

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