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An athlete executing a long jump leaves the ground at a 27.7∘ angle and travels 7.60m.If this speed were increased by just 5.0%, how much longer would the jump be?

  • science -

    Vi = v sin 27.7
    0 = Vi - 9.8 t

    t = v sin 27.7 /9.8 that is time to the top
    total time in air = 2 t
    = 2 v sin 27.7/9.8

    u = v cos 27.7
    d = (v cos 27.7)(2 v sin 27.7 /9.8)
    d = (2 v^2/9.8) cos 27.7 sin 27.7
    but 2 cosA sinA = sin 2A
    d = (v^2/9.8) sin (55.4)
    either do d for v = 7.6 and v=1.05(7.6)
    or take derivative
    d d/dv = (2v sin 55.4)/9.8
    d d = ( 2 v sin 55.4 /9.8) dv

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