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.
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=9405` take square roots
`x approx 96.98`
The prey travels about 97m.
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