Question

    A person throws a ball from ground level at speed u and

    angle θ. The ball reaches maximum height H and range R. What is the ratio H/R?
    A tanθ / 4 Correct Answer Incorrect Answer
    B tanθ / 2 Correct Answer Incorrect Answer
    C tanθ Correct Answer Incorrect Answer
    D cotθ / 4 Correct Answer Incorrect Answer

    Solution

    Given:

    • Maximum height: H = (u²·sin²θ) / (2g)
    • Range: R = (u²·sin2θ) / g
    Now take the ratio H/R: H/R = [(u²·sin²θ) / (2g)] ÷ [(u²·sin2θ) / g] = (sin²θ / 2) ÷ (sin2θ)
    = sin²θ / (2·sin2θ) Now use the identity: sin2θ = 2·sinθ·cosθ So, H/R = sin²θ / [2·(2·sinθ·cosθ)] = sinθ / (4·cosθ) = (1/4)·tanθ

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