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A baseball is thrown horizontally from a cliff at 30 m/s and lands 7 seconds after the baseball was thrown. Calculate the horizontal AND vertical distance.

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whitneytr12

Answer:

The horizontal and vertical distances are x = 210 m and y = -240.35 m, respectively.

Explanation:

Using the equation of the displacement in the x-direction, we have:

(let's recall we have a constant velocity in this direction)

[tex]x=v_{ix}t[/tex]

Where:

  • v(ix) is the initil velocity in the x direction (v(ix) = 30 m/s)
  • t is the time (t = 7 s)

[tex]x=30(7)[/tex]    

[tex]x=210\: m[/tex]    

Now, we need to use the equation of the displacement in the y-direction to find the vertical distance. Here we have an acceleration (g)

[tex]y=v_{iy}t-\frac{1}{2}gt^2[/tex]

Where:

  • v(iy) is the initial velocity at the y-direction. In this case, it will be 0
  • t is the time
  • g is the acceleration of gravity (g=9.81 m/s²)

Then, the vertical position at 7 s is:

[tex]y=-\frac{1}{2}(9.81)(7)^2[/tex]

[tex]y=-240.35\: m[/tex]

Therefore, the horizontal and vertical distances are x = 210 m and y = -240.35 m, respectively. The minus sign means the negative value in the y-direction.

I hope it helps you!

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