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9 February, 16:56

A cat jumps off a table which is 1.5 m high. If the initial velocity of the cat is 10 m/s, at an angle of 37 degrees above the horizontal, how far from the edge of the table does the cat land?

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  1. 9 February, 18:27
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    11.5 m

    Explanation:

    First, find the time it takes to land.

    Given:

    Δy = - 1.5 m

    v₀ = 10 sin 37° m/s

    a = - 9.8 m/s²

    Find: t

    Δy = v₀ t + ½ at²

    -1.5 m = (10 sin 37° m/s) t + ½ (-9.8 m/s²) t²

    -1.5 = 6.02 t - 4.9 t²

    4.9 t² - 6.02 t - 1.5 = 0

    Solve with quadratic formula:

    t = [ - (-6.02) ± √ ((-6.02) ² - 4 (4.9) (-1.5)) ] / 2 (4.9)

    t = 1.44

    Now find how far it moves horizontally in that time:

    Given:

    t = 1.44 s

    v₀ = 10 cos 37° m/s

    a = 0 m/s²

    Find: Δx

    Δx = v₀ t + ½ at²

    Δx = (10 cos 37° m/s) (1.44 s) + ½ (0 m/s²) (1.44 s) ²

    Δx = 11.5 m

    The cat lands 11.5 meters from the table.
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