Exercício de Dinamica (121)

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132 
 
PROBLEM 11.89 
A ball is thrown so that the motion is defined by 
the equations 5x t= and 22 6 4.9 ,y t t= + − where 
x and y are expressed in meters and t is expressed 
in seconds. Determine (a) the velocity at t 1s,= 
(b) the horizontal distance the ball travels before 
hitting the ground. 
 
SOLUTION 
Units are meters and seconds. 
Horizontal motion: 5x
dx
v
dt
= = 
Vertical motion: 6 9.8y
dy
v t
dt
= = − 
(a) Velocity at t = 1 s. 5
6 9.8 3.8
x
y
v
v
=
= − = −
 
 
2 2 2 25 3.8 6.28 m/s
3.8
tan 37.2
5
x y
y
x
v v v
v
v
θ θ
= + = + =
−= = = − ° 6.28 m/sv = 37.2°  
(b) Horizontal distance: ( 0)y = 
 
22 6 4.9
1.4971s
(5)(1.4971) 7.4856 m
y t t
t
x
= + −
=
= = 7.49 mx = 