Determinação do Raio de Curvatura

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213 
 
 
PROBLEM 11.144 
A basketball is bounced on the ground at Point A and rebounds with a velocity Av of 
magnitude 2.5 m/s as shown. Determine the radius of curvature of the trajectory 
described by the ball (a) at Point A, (b) at the highest point of the trajectory. 
 
SOLUTION 
 

 
(a) We have 
2
( ) A
A n
A
v
a
ρ
= 
 or 
2
2
(2.5 m/s)
(9.81 m/s ) sin 15
Aρ =
°
 
 or 2.46 mAρ =  
(b) We have 
2
( ) B
B n
B
v
a
ρ
= 
 where Point B is the highest point of the trajectory, so that 
 ( ) sin 15B A x Av v v= = ° 
 Then 
2
2
[(2.5 m/s) sin 15°]
0.0427 m
9.81 m/s
Bρ = = 
 or 42.7 mmBρ = 