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Nathan is walking to the store and sees a snake slithering across the sidewalk. He jumps over it with an initial vertical velocity of 10 ft/s. How long does it take for Nathan to land back on the ground

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Corsaquix

Answer:

[tex]0.62\:\mathrm{s}[/tex]

Explanation:

Since the universal SI unit for velocity is meters/second, let's convert ft/s to m/s:

[tex]10\:\mathrm{ft/s}=3.048\:\mathrm{m/s}[/tex]

We can use the following kinematics equation to solve this question:

[tex]v_f=v_i+at[/tex]

What we know:

  • The initial velocity, [tex]v_i[/tex], is [tex]3.048\:\mathrm{m/s}[/tex]
  • (physics concept) The final velocity must be equal in magnitude but opposite in direction to the initial velocity ([tex]v_f=-3.048\:\mathrm{m/s}[/tex])
  • Acceleration, [tex]a[/tex], is acceleration due to gravity at about [tex]9.8\:\mathrm{m/s}[/tex]

Solving for [tex]t[/tex]:

[tex]-3.048=3.048+(-9.8t),\\-6.096=-9.8t,\\t=\frac{-6.096}{-9.8}\approx \boxed{0.62\:\mathrm{s}}[/tex]

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