You kick a soccer ball with a speed of 31 m/s at an angle of 50°. How long does it take the ball to reach the top of its trajectory?

Question

You kick a soccer ball with a speed of 31 m/s at an angle of 50°. How long
does it take the ball to reach the top of its trajectory?

in progress 0
Cherry 6 months 2021-07-22T01:54:29+00:00 2 Answers 7 views 0

Answers ( )

    0
    2021-07-22T01:55:31+00:00

    Answer:

    2.42

    Explanation:

    0
    2021-07-22T01:55:39+00:00

    All credit goes to the person who answered this years ago:)
    Reaches max height at t = 2.42s.
    Explanation:
    I’ve assumed we are neglecting air resistance. If not let me know and I’ll update.
    We want to examine the behaviour of the ball in the y-direction. In the absence of air resistance the only force acting on the ball is gravity, which produces an acceleration in the negative y direction. From Newton’s 2nd law:
    m
    d
    2
    y
    d
    t
    2
    =

    m
    g
    m
    d
    2
    y
    d
    t
    2
    =

    m
    g
    Integrating:
    d
    y
    d
    t
    =


    g
    d
    t
    d
    y
    d
    t
    =

    g

    t
    +
    C
    From initial conditions,
    d
    y
    d
    t
    =
    v
    y
    (
    t
    )
    ,
    v
    0
    =
    v
    (
    0
    )
    =
    31

    sin
    (
    50
    )

    v
    y
    (
    t
    )
    =
    v
    0

    g

    t
    The maximum height will be reached at
    v
    y
    =
    0
    so we solve for t.
    v
    y
    (
    t
    h
    max
    )
    =
    0

    v
    0
    =
    g

    t
    h
    max
    t
    h
    max
    =
    v
    0
    g
    =
    31

    sin
    (
    50
    )

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