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Vectors and Motion in Two Dimensions

AP Physics 1· difficulty 4/5

A projectile is launched from the ground at v0=20 m/sv_0 = 20\text{ m/s} and θ=40°\theta = 40° and lands on a roof h=5 mh = 5\text{ m} higher. How far horizontally does it travel before landing? Use g=9.8 m/s2g = 9.8\text{ m/s}^2.

  • A

    32.7 m

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  • B

    27.0 m

  • C

    40.4 m

  • D

    21.6 m

Explanation

Components: v0x≈15.32v_{0x} \approx 15.32, v0y≈12.86v_{0y} \approx 12.86. Solve 5=12.86t−4.9t25 = 12.86 t - 4.9 t^2. Roots: t=(12.86±165.4−98)/9.8t = (12.86 \pm \sqrt{165.4 - 98})/9.8. Take later root ≈2.13 s\approx 2.13\text{ s}. Then x=15.32×2.13≈32.7 mx = 15.32 \times 2.13 \approx 32.7\text{ m}.

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