An unwary football player collides with a padded goalpost while running at a velocity of 9.50 m/s and comes to a full stop after compressing

Question

An unwary football player collides with a padded goalpost while running at a velocity of 9.50 m/s and comes to a full stop after compressing the padding and his body 0.250 m.
(a) How long does the collision last?
(b) What is his deceleration?

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Bơ 5 years 2021-09-01T01:45:49+00:00 1 Answers 29 views 0

Answers ( )

  1. ngockhue
    0
    2021-09-01T01:46:56+00:00
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    Answer:

    (a) The collision lasts for 0.053 s.

    (b) The deceleration is 180.5 m/s².

    Explanation:

    Given:

    Initial velocity of the player (u) = 9.50 m/s

    Final velocity of the player (v) = 0 m/s (Comes to a stop)

    Displacement of the player (S) = 0.250 m

    We know that, using equation of motion relating displacement (S), acceleration (a), initial velocity (u) and final velocity (v), we have:

    v^2=u^2+2aS

    Expressing in terms of ‘a’, we get:

    a=\frac{v^2-u^2}{2S}

    Plug in the given values and solve for ‘a’. This gives,

    a=\frac{0-9.50^2}{2\times 0.250}\\\\a=\frac{-90.25}{0.5}=-180.5\ m/s^2

    Therefore, the acceleration of the player is -180.5 m/s². So, the deceleration is 180.5 m/s².

    Now, using the first equation of motion, we have:

    v=u+at\\\\t=\frac{v-u}{a}

    Plug in the given values and solve for ‘t’. This gives,

    t=\frac{0-9.5}{-180.5}\\\\t=0.053\ s

    Therefore, the the collision will last for 0.053 s.

    (a) The collision lasts for 0.053 s.

    (b) The deceleration is 180.5 m/s².

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