Two tugboats are towing a ship.Each exerts a force of 6000 N and the angle between two ropes is 60 degrees.What is the resultant force on the ship?

8 answers

F(net)= 2F•cos30°

10400

Fr = 6000[0o] + 6000[60o]
Fr = 6000 + 3000+5196i = 9000 + 5196i =
Fr = Sqrt(9000^2 + 5196^2).

10392 N

We need to use law of parallelogram of vector addition. For two vectors
→
P
and
→
Q
having an angle
θ
between the two the resultant vector
→
R
is given by
∣
∣
∣
→
R
∣
∣
∣
=
√
∣
∣
∣
→
P
∣
∣
∣
2
+
∣
∣
∣
→
Q
∣
∣
∣
2
+
2
∣
∣
∣
→
P
∣
∣
∣
∣
∣
∣
→
Q
∣
∣
∣
cos
θ

and angle of the resultant
α
=
tan
−
1
⎛
⎜
⎜
⎜
⎝
∣
∣
∣
→
Q
∣
∣
∣
sin
θ
∣
∣
∣
→
P
∣
∣
∣
+
∣
∣
∣
→
Q
∣
∣
∣
cos
θ
⎞
⎟
⎟
⎟
⎠
Inserting given values we get
∣
∣
∣
→
R
∣
∣
∣
=
√
(
6000
)
2
+
(
6000
)
2
+
2
×
6000
×
6000
×
cos
60

⇒
∣
∣
∣
→
R
∣
∣
∣
=
√
(
6000
)
2
+
(
6000
)
2
+
2
×
6000
×
6000
×
0.5

⇒
∣
∣
∣
→
R
∣
∣
∣
=
6000
√
3

⇒
∣
∣
∣
→
R
∣
∣
∣
=
10392.3
N
rounded to one decimal place.
and
α
=
tan
−
1
(
6000
×
sin
60
6000
+
6000
cos
60
)

⇒
α
=
tan
−
1
⎛
⎜
⎝
√
3
2
1
+
1
2
⎞
⎟
⎠

⇒
α
=
tan
−
1
(
1
√
3
)

⇒
α
=
30
∘
measured as per measurement of
∠
θ