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2 April, 19:13

Salmon often jump waterfalls to reach their breeding grounds.

Starting downstream, 1.88 m away from a waterfall 0.262 m in height, at what minimum speed must a salmon jumping at an angle of 43.5° leave the water to continue upstream?

The acceleration due to gravity is 9.81 m/s^2.

Answer in units of m/s.

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Answers (1)
  1. 2 April, 20:35
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    4.65 m/s

    Explanation:

    Given:

    θ = 43.5°

    Δx = 1.88 m

    Δy = 0.262 m

    aₓ = 0 m/s²

    aᵧ = - 9.81 m/s²

    Find: v₀

    Δx = v₀ₓ t + ½ aₓ t²

    (1.88 m) = (v₀ cos 43.5°) t + ½ (0 m/s²) t²

    t = 1.88 m / (v₀ cos 43.5°)

    t = 2.59 m / v₀

    Δy = v₀ᵧ t + ½ aᵧ t²

    (0.262 m) = (v₀ sin 43.5°) t + ½ (-9.81 m/s²) t²

    Substitute:

    0.262 m = (v₀ sin 43.5°) (2.59 m / v₀) + ½ (-9.81 m/s²) (2.59 m / v₀) ²

    0.262 m = 2.59 m sin 43.5° - 32.9 m³/s² / v₀²

    v₀ = 4.65 m/s
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