Exercício de Dinamica (141)

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152 
 
PROBLEM 11.104 
A golfer hits a golf ball with an initial velocity of 160 ft/s at an angle of 25° with the horizontal. Knowing that 
the fairway slopes downward at an average angle of 5°, determine the distance d between the golfer and Point B 
where the ball first lands. 
 
 
SOLUTION 
First note 0
0
( ) (160 ft/s)cos 25
( ) (160 ft/s)sin 25
x
y
v
v
= °
= °
 
and at B cos 5 sin 5B Bx d y d= ° = − ° 
Now Horizontal motion. (Uniform) 
 00 ( )xx v t= + 
At B 
cos 5
cos 5 (160 cos 25 ) or
160 cos 25Bd t t d
°° = ° =
°
 
 Vertical motion. (Uniformly accelerated motion) 
 2 2
0
1
0 ( ) ( 32.2 ft/s )
2yy v t gt g= + − = 
At B: 21
sin 5 (160 sin 25 )
2B Bd t gt− ° = ° − 
Substituting for Bt 
2
2cos 5 1 cos 5
sin 5 (160 sin 25 )
160 cos 25 2 160 cos 25
d d g d
   ° °− ° = ° −   ° °   
 
or 22
(160 cos 25 ) (tan 5 tan 25 )
32.2 cos 5
726.06 ft
d = ° ° + °
°
=
 
or 242 ydd = 