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6 April, 23:41

The acceleration due to gravity on Earth is 32 ft/sec2. A tomato is dropped from 100 feet above the ground. Give units in your answers. (a) At what speed does the tomato hit the ground? (b) How long does it take for the tomato to travel the last 10 feet? Give your answer as a decimal approximation with units.

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  1. 7 April, 00:07
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    a) the final velocity is v=80 ft/s

    b) the time required is 2.5 seconds

    Step-by-step explanation:

    The final velocity is related with the acceleration through

    v² = v₀² + 2*g*h

    where

    v₀ = initial velocity = 0 (dropped from test)

    g = acceleration

    h = height

    replacing values

    v² = v₀² + 2*g*h = 0² + 2*32 ft/s² * 100 ft = 6400 ft²/s²

    then

    v = √6400 ft²/s² = 80 ft/s

    the tomato hit the ground at v=80 ft/s

    h₀ = h + v₀*t - 1/2*g*t²

    since h₀=0 (initial height) and v₀=0

    0 = h - 1/2*g*t²

    t = √ (2*h/g)

    replacing values

    t = √ (2*h/g) = √ (2*100 ft / 32 ft/s²) = 10/4 s = 2.5 s

    t = 2.5 seconds
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