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An unwary football player collides head-on with a padded goalpost while running at 7.5 m/s and comes to a full stop after compressing the padding and his body by 0.27 m. Take the direction of the player’s initial velocity as positive.1.assuming constant acceleration calculate the his acceleration during the collision in meters per second squared.2 how long does the collision last in seconds.

Respuesta :

Answers:

1. a = -104.16 m/s²

2. t = 0.072

Explanation:

To find the acceleration, we will use the following equation:

[tex]v^2_f=v^2_i+2ax[/tex]

where vf is the final velocity, vi is the initial velocity, a is the acceleration and x is the distance. So, replacing vf by 0 m/s, vi by 7.5 m/s, and x by 0.27m, we get:

[tex]\begin{gathered} 0^2=7.5^2+2a(0.27) \\ 0=56.25+0.54a \end{gathered}[/tex]

Then, solving for a, we get:

[tex]\begin{gathered} 0-56.25=56.25+0.54a-56.25 \\ -56.25=0.54a \\ \frac{-56.25}{0.54}=\frac{0.54a}{0.54} \\ -104.16m/s^2=a \end{gathered}[/tex]

Therefore, the acceleration during the collision is -104.16 m/s²

Then, to calculate how long the collision last, we will use the following equation:

[tex]v_f=v_i+at[/tex]

So, replacing the values and solving for t, we get:

[tex]\begin{gathered} 0=7.5-104.16t \\ 104.15t=7.5 \\ t=\frac{7.5}{104.15}=0.072s \end{gathered}[/tex]

Therefore, the collision last 0.072 seconds

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