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Q2.5-33PE

Expert-verifiedFound in: Page 35

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**An unwary football player collides with a padded goalpost while running at a velocity of ****7.50 m/s and comes to a full stop after compressing the padding and his body 0.350****. **

**(a) What is his deceleration? **

**(b) How long does the collision last?**** **

a) -80.36 m/s^{2}

b) 0.0933 s

- The initial velocity of the football, U = 7.50 m/s.
- The final velocity of the football, V = 0 m/s.
- The distance traveled in compressing the padding, D = 0.350 m.

**a) The deceleration of the football can be calculated using the equation as:**

**${V}^{2}-{U}^{2}=2ad$ ****Here V is the final velocity, U is the initial velocity, a is the acceleration, and d is the distance traveled**.

Substituting values in the above expression, we get,

$(0{)}^{2}-(7.5{)}^{2}=2\times (0.35)\times a\phantom{\rule{0ex}{0ex}}-56.25=2\times (0.35)\times a\phantom{\rule{0ex}{0ex}}a=\frac{-56.25}{2\times (0.35)}\phantom{\rule{0ex}{0ex}}a=-80.357{\text{m/s}}^{\text{2}}$

The deceleration of the football is -80.357 m/s^{2}.

**b) The time required can be calculated as:**

**V = U + at **

**Here V is the final velocity, U is the initial velocity, a is the acceleration, and t is the time.**

** **

Substituting values in the above expression, we get,

** $0=7.5+(-80.36)\times t\phantom{\rule{0ex}{0ex}}t=\frac{7.5}{80.36}\phantom{\rule{0ex}{0ex}}t=0.0933\text{s}$**

Hence the time period is 0.0933 s.

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