# physics

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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?

• physics -

F(net)= 2F•cos30°

• physics -

10400

• physics -

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

• physics -

10392 N

• Physics -

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

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