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Chapter 2: Q2.5-33PE (page 35)

An unwary football player collides with a padded goalpost while running at a velocity of7.50 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?

Short Answer

Expert verified

a) -80.36 m/s2

b) 0.0933 s

Step by step solution

01

Given Data

  • 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.
02

Deceleration and time period

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

V2-U2=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×(0.35)×a-56.25=2×(0.35)×aa=-56.252×(0.35)a=-80.357m/s2

The deceleration of the football is -80.357 m/s2.

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)×tt=7.580.36t=0.0933s

Hence the time period is 0.0933 s.

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