hunkyle76
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Rodney hits a 0.060 kg tennis ball straight up with a speed of 15 m/s from a height of 2.2 m above the ground. How fast is the ball going when it is 9.5 m above the ground?

Respuesta :

Answer:

Explanation:

From the question we are told that

   The mass of the tennis ball is  [tex]m = 0.060 \ kg[/tex]

    The speed is  [tex]u = 15 \ m/s[/tex]

    The initial height of the ball is  [tex]h_o = 2.2 \ m[/tex]

     The height considered is  [tex]h = 9.5 \ m[/tex]

Generally the time taken to reach the considered height is mathematically evaluated from the equation of motion as follows

           [tex]h = h_o + ut - \frac{1}{2} gt^2[/tex]

=>         [tex]9.5 = 2.2 + 15t - \frac{1}{2} * 9.8 t^2[/tex]

=>         [tex]7.3 = 15t - 4.9t^2[/tex]

=>          [tex]4.9t^2 -15t + 7.3[/tex]

solving the above equation using quadratic formula

           [tex]t= 0.6070 \ s[/tex] and  [tex]t_1 = 2.454 \ s[/tex]

Generally from kinematic equation we have that

        [tex]v = u - gt[/tex]

=>     [tex]v= 15 - 9.8 * 0.6070[/tex]

=>      [tex]v= 9.0514 \ m/s[/tex]

Note if we had used the second values of time the velocity at 9.5 \ m would have been negative which is not correct given that at maximum height velocity is zero