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It will take the quarter 0.151 seconds to reach the ground.
Given the following data:
We know that acceleration due to gravity (a) for an object is equal to 9.8 meter per seconds square.
To find how much time it will take the quarter to reach the ground, we would use the second equation of motion.
Mathematically, the second equation of motion is given by the formula;
[tex]S = ut + \frac{1}{2} at^2[/tex]
Where:
Substituting the values into the formula, we have;
[tex]1.45 = 10.32(t) + \frac{1}{2} (9.8)t^2\\\\1.45 = 10.32t + 4.9t^2\\\\4.9t^2 + 10.32t - 1.45 = 0[/tex]
The standard form of a quadratic equation is:
[tex]ax^2 + bx + c = 0[/tex]
a = 4.9, b = 10.32 and c = 1.45
We would solve the above quadratic equation by using the quadratic equation formula;
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]
Substituting the values, we have;
[tex]t = \frac{-10.32\; \pm \;\sqrt{10.32^2\; - \;4(4.9)(1.45)}}{2(4.9)}\\\\t = \frac{-10.32\; \pm \;\sqrt{106.5024\; - \;28.42}}{9.8}\\\\t = \frac{-10.32\; \pm \;\sqrt{78.0824}}{9.8}\\\\t = \frac{-10.32\; \pm \;8.84}{9.8}\\\\t = \frac{-10.32\; + \;8.84}{9.8}\\\\t = \frac{1.48}{9.8}[/tex]
Time, t = 0.151 seconds.
Therefore, it will take the quarter 0.151 seconds to reach the ground.
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