m1 vector q, may 2004

a small boat, S drifting in the sea, is modelled asa particle moving in a straight line at constant speed. When first sighted at 0900, S is at apoint with position vector (4i- 6j) km relative to a fixed origin O. At 0945, S is at the point with position vector(7i- 7.5j)km. at time t hours after 0900, S is at the point with position vector s km.

a) calculate the bearing on which S is drifting
b) find an expresion for s in terms of t

AT 1000 a motor boat M leaves 0 an travels with constant velocity (pi +qj) km h^-1. given that M intercepts S at 1015

c) calculatethe value of p and the value of q.

please, ive got no idea what to do, i cant do vectors! :frown:

Reply 1

Christophicus

18

ruth_lou

a small boat, S drifting in the sea, is modelled asa particle moving in a straight line at constant speed. When first sighted at 0900, S is at apoint with position vector (4i- 6j) km relative to a fixed origin O. At 0945, S is at the point with position vector(7i- 7.5j)km. at time t hours after 0900, S is at the point with position vector s km.

a) calculate the bearing on which S is drifting
b) find an expresion for s in terms of t

AT 1000 a motor boat M leaves 0 an travels with constant velocity (pi +qj) km h^-1. given that M intercepts S at 1015

c) calculatethe value of p and the value of q.

please, ive got no idea what to do, i cant do vectors! :frown:

a) To calculate a bearing you use trigonometry.
Firstly you have to calculate the relative displacements.
So, (7i - 7.5j) - (4i - 6j) = 3i - 1.5j

Now you have to calculate the bearing relative to north (j vector)
So, tan^-1 1.5/3 = 26.6 degrees.

You now have to add on 90 degrees to get the bearing from north.
So 26.6 degrees + 90 = 117 degrees (3sf) east of north.

b) To calculate s in terms of t.
You need to calculate how far the boat travels per hour in vector form.
Boat travels (3i- 1.5j)km in 45 mins which is 3/4 of 1 hour.
So (3i - 1.5j)*4/3 = distance travelled by boat in one hour = (4i - 2j)km

You also have to add on the intial position vector.
(4i - 6j) + (4i - 2j)t km
t = 1 hour.

c) At 1015, t = 1.25 (hours)
When the boats intercept, their displacements are equal.

s (M) : (pi + qj)*1.25
s (S) calculated in b: (4i - 6j) + (4i - 2j)*1.25

1.25pi + 1.25qj = (4i - 6j) + (4i - 2j)*1.25
1.25pi + 1.25qj = 4i - 6j + 5i - 2.5j
1.25pi + 1.25qj = 9i - 8.5j

1.25p = 9
1.25q = -2.5

Therefore;
p = 7.2
q = -2

Reply 2

Gaz031

15

AT 1000 a motor boat M leaves 0 an travels with constant velocity (pi +qj) km h^-1. given that M intercepts S at 1015
c) calculatethe value of p and the value of q.
please, ive got no idea what to do, i cant do vectors! :frown:

Using the above post you can calculate s (and therefore M) at 1015.
You know that M took 0.25hrs to travel the distance to the displacement s ( it starts from O)

S=ut + 0.5at^2
(position M at 1015) = (pi+qj)(0.25)
Compare the coefficients of the i and j values to get the necessary information.

m1 vector q, may 2004

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