A rock is thrown upwards from the roof of an 15.0m high building at 30m/s at an angle of 33 degrees. Find the speed of the rock when it stri

Question

A rock is thrown upwards from the roof of an 15.0m high building at 30m/s at an angle of 33 degrees. Find the speed of the rock when it strikes the ground.

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Kiệt Gia 4 years 2021-08-18T21:51:13+00:00 1 Answers 26 views 0

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  1. huyenthanh
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    2021-08-18T21:53:10+00:00
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    Answer:

    The speed of the rock when it strikes the ground is 34.55 m/s

    Explanation:

    Given;

    height of the building, h = 15 m

    initial velocity of the rock, V₀ = 30 m/s

    angle of projection, θ = 33°

    The velocity of the rock before it strikes the ground, can be calculated from vertical component of the velocity and horizontal component of the velocity.

    Vertical component of the velocity,V_y

    V_y^2 = (V_oSin \theta)^2 + 2gh\\\\V_y^2 = (30Sin \ 33)^2 + 2(9.8)(15)\\\\V_y^2 = 266.93 + 294\\\\V_y = \sqrt{560.93} \\\\V_y = 23.684 \ m/s

    Horizontal component of the velocity, V_x

    V_x = V_0 Cos\theta\\\\V_x = 30Cos33\\\\V_x = 25.161 \ m/s

    The velocity of the rock when it strikes the ground, V

    V = \sqrt{V_y^2 + V_x^2} \\\\V = \sqrt{23.684^2 + 25.161^2} \\\\V = 34.55 \ m/s

    Therefore, the speed of the rock when it strikes the ground is 34.55 m/s

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