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215 
 
 
PROBLEM 11.146 
Three children are throwing snowballs at each other. Child A 
throws a snowball with a horizontal velocity v0. If the snowball 
just passes over the head of child B and hits child C, determine 
the radius of curvature of the trajectory described by the snowball 
(a) at Point B, (b) at Point C. 
 
SOLUTION 
The motion is projectile motion. Place the origin at Point A. 
Horizontal motion: 0 0x v x v t= =v 
Vertical motion: 0 0, ( ) 0yy v= = 
 21
2yv gt y gt= − = − 
 
2
,
h
t
g
= where h is the vertical distance fallen. 
 | | 2yv gh= 
Speed: 2 2 2 2
0 2x yv v v v gh= + = + 
Direction of velocity. 
 0cos
v
v
θ = 
Direction of normal acceleration. 
 
2
0cosn
gv v
a g
v
θ
ρ
= = = 
 
Radius of curvature: 
3
0
v
gv
ρ = 
At Point B, 1 m; 7 mB Bh x= = 
 
2
(2)(1 m)
0.45152 s
9.81 m/s
Bt = = 
 
0 0
2 2 2 2
7 m
15.504 m/s
0.45152 s
(15.504) (2)(9.81)(1) 259.97 m /s
B
B B
B
B
x
x v t v
t
v
= = = =
= + =