Mechanics + Pure- Please Help

Hi guys, can i have some help with these three.... (pure one at bottom)

1) Two small smooth balls C and D are of equal radius and have masses m and 3m respectively. They are also moving towards each other on a smooth horizontal table and collide directly. The speeds of C and D immediately before the collision and 3u and u respecively. In the collision between C and D, the kinetic energy lost is 9/2mu^2.

a) Find the speed of C immediately after colliding with D.
b) State whether the direction of motion of C is changed by the collision with D, giving a reason for your answer.

and

Two motor boats A and B ar moving with constant velocities. The velocity of A is 30km/h due north, and B is moving at 20 km/h on a bearing of 60 degrees. The unit vectors i and j are directed due east and north respectively. At 10am the position vector of B is 70j km relative to a fixed origin O and A is at the point 0; t hours later the position vectors of A and B are r km and s km respetively.

a) Find the velocity of B in the form (pi+qj) km/h

(This turned out to be 10i+17.32j)

b) Find expressions for r and s in terms of t.

The boats can maintain radio contact with each other provided that the distance between them is no more than 70 km.

c) Find the time at which the boats are again at the maximum distance at which they can maintain radio contact with eachother.

PURE

2x^2+px-3p

a) Find in terms of P the solutions to the above equation:

I got (2x+3p)(x-p), x=-3/2p and p

but (this where i just froze, and i dont think its that hard, i just forgot)

b) Find the range of values of p for which this equation has two distinct real roots.

Did i just have to do b^2-4.a.c ??

Cheers guys!

Reply 1

faa

anyone :-(? lol