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10 April, 13:48

a missile is moving 1810 m/s at a 20.0. It needs to hit a target 29,500m away in a 65.0 magnitude in 9.20s. What acceleration must its engine produce?

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  1. 10 April, 14:55
    0
    323 m/s²

    Explanation:

    Given:

    x₀ = 0 m

    y₀ = 0 m

    x = 29500 cos 65°

    y = 29500 sin 65°

    v₀x = 1810 cos 20°

    v₀y = 1810 sin 20°

    t = 9.20

    Find:

    ax, ay, θ

    First, in the x direction:

    x = x₀ + v₀ t + ½ at²

    29500 cos 32° = 0 + (1810 cos 20°) (9.20) + ½ ax (9.20) ²

    25017 = 15648 + 42.32 ax

    ax ≈ 221.4

    And in the y direction:

    y = y₀ + v₀ t + ½ at²

    29500 sin 32° = 0 + (1810 sin 20°) (9.20) + ½ ay (9.20) ²

    15633 = 5695 + 42.32 ay

    ay ≈ 234.8

    Therefore, the magnitude of the acceleration is:

    a² = ax² + ay²

    a² = (221.4) ² + (234.8) ²

    a ≈ 322.7

    Rounded to 3 significant figures, the magnitude of the acceleration is approximately 323 m/s².
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