Exercício de Dinamica (38)

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49 
 
 
PROBLEM 11.39 
As relay runner A enters the 20-m-long exchange zone with a 
speed of 12.9 m/s, he begins to slow down. He hands the baton to 
runner B 1.82 s later as they leave the exchange zone with the 
same velocity. Determine (a) the uniform acceleration of each of 
the runners, (b) when runner B should begin to run. 
 
SOLUTION 
(a) For runner A: 2
0
1
0 ( )
2A A Ax v t a t= + + 
 At 1.82 s:t = 21
20 m (12.9 m/s)(1.82 s) (1.82 s)
2 Aa= + 
 or 22.10 m/sAa = −  
 Also 0( )A A Av v a t= + 
 At 1.82 s:t = 2
1.82( ) (12.9 m/s) ( 2.10 m/s )(1.82 s)
9.078 m/s
Av = + −
=
 
 For runner B: [ ]2 0 2 0B B Bv a x= + − 
 When 220 m, : (9.078 m/s) 2 (20 m)B B A Bx v v a= = = 
 or 22.0603 m/sBa = 
 22.06 m/sBa =  
(b) For runner B: 0 ( )B B Bv a t t= + − 
 where Bt is the time at which he begins to run. 
 At 1.82 s:t = 29.078 m/s (2.0603 m/s )(1.82 )sBt= − 
 or 2.59 sBt = − 
 Runner B should start to run 2.59 s before A reaches the exchange zone. 