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26 August, 22:28

A 1.7-kg firework is fired from the ground straight up on a planet with whose acceleration due to gravity is 4.8 m/s/s. You want the firework to explode when it is at a height of 165 m. You want the firework to be moving down at a speed of 10.0 m/s when it explodes. Use this information to find out how fast you should launch your firework and how much time you should have on your trigger.

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  1. 26 August, 22:48
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    41.0 m/s, 10.6 s

    Explanation:

    Given:

    a = - 4.8 m/s²

    Δy = 165 m

    v = - 10.0 m/s

    Find: v₀ and t

    v² = v₀² + 2aΔy

    (-10.0 m/s) ² = v₀² + 2 (-4.8 m/s²) (165 m)

    v₀ = 41.0 m/s

    Δy = vt - ½ at²

    165 m = (-10.0 m/s) t - ½ (-4.8 m/s²) t²

    165 = - 10t + 2.4t²

    0 = 2.4t² - 10t - 165

    Solve with quadratic formula:

    t = [ - (-10) ± √ ((-10) ² - 4 (2.4) (-165)) ] / 2 (2.4)

    t = (10 ± √1684) / 4.8

    t = 10.6 s
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