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A hawk flying at 19 m/s at an altitude of 165 m accidentally drops its prey. How far does the prey travel if its trajectory is a parabola?   The parabolic trajectory of the falling prey is described by the equation y=165-(x^2)/57 until it hits the ground, where y is its height above the ground and x is the horizontal distance traveled in meters. Calculate the distance traveled by the prey from the time it is dropped until the time it hits the ground.

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lfryerda eNotes educator | Certified Educator

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To determine the horizontal distance travelled, we set y=0 and solve for x:

`y=165-x^2/57`   let y=0

`0=165-x^2/57`   move variable to left side

`x^2/57=165`   multiply by 57

`x^2=165(57)`

`x^2=9405`   take square roots

`x=sqrt9405`

`x approx 96.98`

The prey travels about 97m.

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