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A ball is thrown vertically upward, which is the positive direction. A little while later it returns to its point of release. The ball is in the air for a total time of 10 s. Note: Near the earth's surface, g is approximately 9.80 m /s2.

What is the algebraic expression for the initial velocity v0 of the ball? Express your answer in terms of the ball's displacement y, its acceleration a in the vertical direction, and the elapsed time t.

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AMB000

Answer:

[tex]v_0=\frac{y}{t}-\frac{at}{2}[/tex]

[tex]v_0=49m/s[/tex]

Explanation:

We can start from the known formula:

[tex]y=y_f-y_0=v_0t+\frac{at^2}{2}[/tex]

so we can write, since we want the initial velocity in terms of the ball's displacement, its acceleration in the vertical direction, and the elapsed time:

[tex]v_0=\frac{y}{t}-\frac{at}{2}[/tex]

and for our values we have:

[tex]v_0=\frac{0m}{10s}-\frac{(-9.8m/s^2)(10s)}{2}=49m/s[/tex]

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