We solve the problem by drawing a free body diagram:
Solution 1
Now we find the sum of the
x
and
y
components of all three forces:
F
x = 20 + 30 cos 45 = 41.2
F
y = 10 + 30 sin 45 = 31.2
And sum these two vectors. The magnitude of the resultant force is
given by:
And the direction is given by:
θ = tan-1(31.2/41.2) = 37.1
o
, North of East.
Thus the object experiences a force of 51.7 Newtons, directed
37.1
o
North of East.
Now we must find its acceleration, using Newton's Second Law:
a =

=

= 5.17

, 37.1
o
North of East
To find the final velocity and position of the object, we simply use
the equations learned in
kinematics:
v
f = v
o + at = 0 + (5.17)(10) = 51.7 m/s
x
f = x
o + v
o
t + (1/2)at
2 = 0 + 0 + (1/2)(5.17)(10)2 = 258.5 m
Thus, after 10 seconds, the object is moving with a velocity of 51.7
m/s, directed
31.7 degrees North of East. Also, the object has moved 258.5 meters, in
the same
direction.