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21 March, 04:14

A cannon tilted up at a 30 angle fires a cannon ball at 80 m/s from atop a 10-m-high fortress wall. what is the ball's impact speed on the ground below?

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  1. 21 March, 07:21
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    To find the velocity of the bullet just before reaching the ground, we use the formula.

    Vy = Vosen (30 °) + gt (1).

    For that we need to know the time it takes for the bullet to reach the ground from the moment it is fired.

    For that we use the formula:

    Xy = Xo + Vosen (30 °) * t + 0.5gt ^ 2 (2)

    where:

    Vy = Component of the speed in the y direction (vertical)

    Vo = initial velocity of the bullet at the exit of the cannon

    g = acceleration of gravity

    Xy = vertical component of the position.

    Xo = initial position.

    t = time.

    To find the time it takes for the bullet to reach the ground, we make Xy = 0 and clear t.

    then it would be:

    0 = 10 + 80sen (30 °) * t + 0.5 * ( - 9.8) t ^ 2.

    The solution to that equation is:

    t = 8.4 seconds.

    We substitute that time in equation (1) and clear Vy.

    We have left:

    Vy = 80 * sin (30 °) + 9.8 * (8.4)

    Vy = 42.38 m / s
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