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Ball A is projected vertically upward at 30 m/s from a point P. Four seconds later, ball B is also launched vertically upwards from the same point P and also at 30 m/s. For how long has ball A been in motion when two balls collide

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onyebuchinnaji

The time of motion of ball A before they collide is 5.1 seconds.

Time of  motion

The two balls will collide at a time "t" when they attain a certain height "h".

The equation of motion

The equation of motion of the two balls is given as follows;

when they collide;

  • A would have traveled, (t + 4) seconds
  • B would have traveled t seconds

[tex]h_A = 30(t+ 4) - \frac{1}{2} g(t+ 4)^2\\\\h_B = 30t - \frac{1}{2} gt^2[/tex]

[tex]h_B = h_A\\\\30t - \frac{1}{2} gt^2 = 30(t + 4) - \frac{1}{2} g(t + 4)^2\\\\30t - \frac{1}{2} gt^2 = 30t + 120- \frac{1}{2}gt^2- 4gt -8g\\\\0 = 120 -4gt -8g\\\\4gt +8g = 120\\\\4(9.8)t + 8(9.8) = 120\\\\39.2t + 78.4 = 120\\\\39.2 t = 41.6\\\\t = \frac{41.6}{39.2} \\\\t = 1.1 \ s[/tex]

Thus, the time of motion of ball A before they collide is (1.1 + 4) = 5.1 seconds.

Learn more about time of motion here: https://brainly.com/question/2364404

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