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Parabolic Trajectory Distance of Dropped Prey

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abbasbhagat4

A hawk drops its prey from an altitude of 220 meters while flying horizontally at 40 meters per second. The prey's trajectory is described parametrically by equations relating its horizontal and vertical positions over time. The distance traveled by the prey can be calculated by setting the vertical position equation equal to 0 when it hits the ground and solving for time, then plugging that time back into the horizontal position equation.

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A hawk flying at 40 m/s at an altitude of 220 m accidentally drops its prey. The parabolic trajectory of the falling prey is described parametrically by x=40t, y=220-4.9t^2 until it hits the ground. The variable X represents the horizontal distance traveled by the prey and the variable Y represents its height above the ground. Calculate the distance traveled by the prey from the time it is dropped until it hits the ground. Express your answer correct to the nearest tenth of a meter. Solution From a physics perspective, the prey hits the ground at y=0. Plugging that into your second equation, 0=220-4.9t^2 t=(220/4.9) Plug that t-value into the x=40t, and voila!

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Parabolic Trajectory Distance of Dropped Prey

  • 1. A hawk flying at 40 m/s at an altitude of 220 m accidentally drops its prey. The parabolic trajectory of the falling prey is described parametrically by x=40t, y=220-4.9t^2 until it hits the ground. The variable X represents the horizontal distance traveled by the prey and the variable Y represents its height above the ground. Calculate the distance traveled by the prey from the time it is dropped until it hits the ground. Express your answer correct to the nearest tenth of a meter. Solution From a physics perspective, the prey hits the ground at y=0. Plugging that into your second equation, 0=220-4.9t^2 t=(220/4.9) Plug that t-value into the x=40t, and voila!