SOLVE:
A tennis ball hit vertically upward has an initial velocity of 8m/s. The height y reached by the ball after x seconds is denoted y=8x-[tex]x^{2}[/tex].
What values of x is the object at or above a height of 15m?

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XYUSHIIN XYUSHIIN · Answer 1

ANSWER

5secs and 3secs

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KIZUNAHIGHIN KIZUNAHIGHIN · Answer 2

[tex]\large \bold {SOLUTION}[/tex]

[tex]\small\textsf{Let y = 15 and rearrange the terms}[/tex]

[tex]\small\sf{y = 8x - {x}^{2} }[/tex]

[tex]\small\sf{15 = 8x - {x}^{2} }[/tex]

[tex]\small\sf{15 + ( - 15)= 8x - {x}^{2} + ( - 15)}[/tex]

[tex]\small\sf{ {x}^{2} - 8x + 15 = 0 }[/tex]

[tex]\small\textsf{Solve the quadratic equation and find x}[/tex]

[tex]\small\sf{ {x}^{2} - 8x + 15 = 0 }[/tex]

[tex]\small\sf{ {x}^{2} - 3x - 5x + 15 = 0 }[/tex]

[tex]\small\sf{ x(x - 3) - 5(x - 3) = 0 }[/tex]

[tex]\small\sf{ (x - 3)(x - 5 ) = 0 }[/tex]

[tex]\small\sf{ x - 3 = 0 }[/tex]

[tex]\small\sf{ x - 3 + 3 = 0 + 3 }[/tex]

[tex]\small\boxed{\green{\sf{x = 3s }}}[/tex]

[tex]\small\sf{x - 5 = 0}[/tex]

[tex]\small\sf{x - 5 + 5 = 0 + 5}[/tex]

[tex]\small\boxed{\green{\sf{x = 5s }}}[/tex]

[tex]\small\textsf{Both are positive values, therfore both are solutions}[/tex]

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