Q2.5-33PE - College Physics (Urone)

Question

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? 

Step-by-Step Solution

Answer

a) -80.36 m/s²

b) 0.0933 s

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.

 

Deceleration and time period

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,

 $$\begin{gathered} (0{)}^2-(7.5{)}^2=2\times (0.35)\times a \\ -56.25=2\times (0.35)\times a \\ a=\frac{-56.25}{2\times (0.35)} \\ a=-80.357 {\text{m/s}}^{\text{2}} \end{gathered}$$

 

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,

 $$\begin{gathered} 0=7.5+(-80.36)\times t \\ t=\frac{7.5}{80.36} \\ t=0.0933 \text{s} \end{gathered}$$

Hence the time period is 0.0933 s.