Thread: A level Maths 05- cont.

this is the rest of the homework .thank you

Hello, carlasader!

Here's #7 . . .

7. Two cars A and B are moving on straight horizontal roads with constant velocities.
The velocity of A is 20 m/sec due east, the velocity of B is m/sec,
where and are unit vectors directed due east and due north, respectively.
Initially A is at the origin O, and the position vector of B is .
At time seconds, the position vectors of A and B are and , resp.

a) Find expressions for and in terms of .

b) Hence write an expression for in terms is .

We have: .

Then: .

c) Find the time when the bearing of B from A is .

Since B is always on a bearing of 45°, this occurs when:
. . Then: . seconds.

d) Find the time when the cars are again 300 m apart.

The distance is: .

If

Square both sides: .

Factor: .


Therefore, they are 300 m apart (again) when seconds.

a) As the forces acting on B are -3mg and T, and the accelleration of the
particle is -(1/2)g, the tension must be (1/2)3mg. That is we have:

-3mg + T = 3ma,

so:

T = 3ma + 3mg

but a= -(1/2)g.

b) Resolve the gravitational force on A into components up the plene and
normal to the plane.

The component normal to the plane is -mg sin(theta), and up the plane is
-mg cos(theta), also sin(theat)=3/5, and cos(theta)=4/5.

Now the forces on the particle up the plane are T = (3/2)mg, the component
of the weight acting up the plane -(4/5)mg, and the friction -mu (3/5)mg

So the total force up the plane is:

T - (4/5)mg - mu (3/5)mg

and the acceleration up the plane is (1/2)g, so:

(3/2)mg - (4/5)mg - mu (3/5)mg = (1/2) mg

or cancelling mg:

(3/2) - (4/5) - mu (3/5) = (1/2)

Which I will leave to the reader to finish.

RonL