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Displacement, Velocity, and Acceleration

AP Physics 1· difficulty 3/5

A helicopter rises at constant 3.0 m/s3.0~\text{m/s}. From it, a package is released at height 30 m30~\text{m} above the ground. Using g≈10 m/s2g \approx 10~\text{m/s}^2, how long does the package take to hit the ground?

  • A

    2.4 s2.4~\text{s}

  • B

    2.8 s2.8~\text{s}

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  • C

    3.0 s3.0~\text{s}

  • D

    3.5 s3.5~\text{s}

Explanation

The package starts moving up at 3 m/s3~\text{m/s}. Solve −30=3t−5t2-30 = 3t - 5 t^2, i.e. 5t2−3t−30=05 t^2 - 3 t - 30 = 0. Quadratic: t=(3+9+600)/10≈(3+24.7)/10≈2.77 st = (3 + \sqrt{9 + 600})/10 \approx (3 + 24.7)/10 \approx 2.77~\text{s}.

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