Vectors and Motion in Two Dimensions

AP Physics 1· difficulty 4/5

v₀ horizontal h R

A projectile is launched horizontally with speed v0v_0 from a cliff of height hh above level ground. Air resistance is negligible. What is the horizontal range RR measured from the base of the cliff to the landing point?

  • A

    v02h/gv_0\sqrt{2h/g}

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  • B

    v0h/gv_0\sqrt{h/g}

  • C

    2v0h/g2v_0\sqrt{h/g}

  • D

    v02ghv_0\sqrt{2gh}

Explanation

Vertical fall time from h=12gt2h = \tfrac{1}{2}gt^2 gives t=2h/gt = \sqrt{2h/g}. Horizontal range is R=v0t=v02h/gR = v_0 t = v_0\sqrt{2h/g}.

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