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