The tip-to-tail triangle shown, or the rectangle, or a tip-to-tail triangle forming the lower half of the rectangle are all correct answers here. F N and F W F N
500 N F N
500 N F W
500 N
[1]
correctly labelled
[1]
= cos(63°)
[1]
= 0.45 so F N = 500 N
!
0.45 = 230 N (2 sig. figs.)
= sin(63°) so F W = 500 N ! sin(63°) = 500 N
!
[1]
0.89 = 450 N
[1]
(Whichever one is done first, the first component correctly calculated gets 2 marks. The repeat calculation for the second component gets 1 mark. The second component can also be found 2
2
2
by Pythagoras’s Pythagoras’ s theorem, as (500 (50 0 N) = ( F N) + ( F W) .) b
As the boat moves forwards, the rudder pushes the water to the left.
[1]
The water pushes the rudder, and hence the stern of the boat, to the right.
[1]
(The directions of the force and what pushes what must be clear in each case.) c
Acceleration is v
2
=
F N
230 N =
130 kg
m
2
2
!2
= 1.8 m s
2
!1 2
[1] 2
= u + 2 as, so 2 as = v ! u = (5.8 m s ) ! 0 = 34 m s 2
34 m s s
a
!2
=
2
34 m s
!2
=
2a
!2
2 " 1.8 m s
!2
= 9.4 m
[1]
(Give 1 mark for applying appropriate equation of motion, which can also be done by using and v = u + at and
then
s = ut +
1 2
2
a t
, and 1 mark for the correct answer.)
It will not go this far as the resultant force is less than 230 N due to drag / resistance forces.
so the component due to the wind must be equal to the drag on the boat from the water (and from the air, although that is much less). e
[1]
The sideways drag from the water is much greater than the forwards drag/ the boat is more streamlined in the forwards direction/ the larger sideways area prevent easy movement in that
f
direction
[1]
Arrow at keel to the right in Figure 1(c).
[1]
Clockwise moment about boat’s centre of gravity = anticlockwise moment about that point F W
1.9 m = F R ! 0.75 m
450 N ! 1.9 m = F R ! 0.75 m, so (Allow own answer to 2
[1]
!
F R
450 N ! 1.9 m =
0.75 m
= 1100 N
[1]
1a for F W.)
Constant speed from A until the route starts to curve.
[1]
As the route curves around B, component of force in forward direction increases,
[1]
which means that the boat speeds up until drag force balances forward force.
[1]
Boat continues at maximum speed along straight part of route up to C.
