Solution]
We use the particle under a net force model and add the forces as vectors. Then Newton’s second law tells us the acceleration.
(a) ∑
F
=
F
1
+
F
2
=(20.0
i
^
+15.0
j
^
)N
Newton’s second law gives, with m=5.00kg
a
=
m
∑
F
=(4.00
i
^
+3.00
j
^
)m/s
2
or a=5.00m/s
2
at θ=36.9
0
(b) In this configuration,
F
2x
=15.0cos60.0
0
=7.50N
F
2y
=15.0sin60.0
0
=13.0N
F
2
=(7.50
i
^
+13.0
j
^
)N
Then,
∑
F
=
F
1
+
F
2
=[20.0
i
^
+(7.50
i
^
+13.0
j
^
)]N
=(27.5
i
^
+13.0
j
^
)N
and
a
=
m
∑
F
=(5.50
i
^
+2.60
j
^
)m/s
2
=6.08m/s
2
=6.08m/s
2
at 25.3
0