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A research group at Dartmouth College has developed a Head Impact Telemetry (HIT) System that can be used to collect data about head accelerations during impacts on the playing field. The researchers observed 249,613 impacts from 423 football players at nine colleges and high schools and collected collision data from participants in other sports. The accelerations during most head impacts (>89%) in helmeted sports caused head accelerations less than a magnitude of 400 m/s2. However, a total of 11 concussions were diagnosed in players whose impacts caused accelerations between 600 and 1800 m/s2, with most of the 11 over 1000 m/s2.Suppose the average speed while stopping was 9 m/s (not necessarily the correct value) and the collision lasted 0.01 s. Find the head's stopping distance (the distance it moves while stopping).

Question

A research group at Dartmouth College has developed a Head Impact Telemetry (HIT) System that can be used to collect data about head accelerations during impacts on the playing field. The researchers observed 249,613 impacts from 423 football players at nine colleges and high schools and collected collision data from participants in other sports. The accelerations during most head impacts (>89%) in helmeted sports caused head accelerations less than a magnitude of 400 m/s2. However, a total of 11 concussions were diagnosed in players whose impacts caused accelerations between 600 and 1800 m/s2, with most of the 11 over 1000 m/s2.

Suppose the average speed while stopping was 9 m/s (not necessarily the correct value) and the collision lasted 0.01 s. Find the head's stopping distance (the distance it moves while stopping).

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Step 1

The final velocity is zero. So, average velocity is,

2
V =18 m/s
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2 V =18 m/s

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Step 2

Now, from Newton’s second law,

та — т
At
=_5
Дt
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та — т At =_5 Дt

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Step 3

Substitute 18 m/s for v...

18 m/s2
a =
(0.01 s
a 1800 m/s2
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18 m/s2 a = (0.01 s a 1800 m/s2

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