Solving Mechanics Problems for Beginners

[Petrulis]

So here are these four mechanics problems. Could anyone help with them because I am quite new to the whole physics world :)

Homework Statement

1) Boat's engine during 1 second can give speed v to L litres of water. What is the maximum speed of boat, if its mass is equal to M?

Homework Equations

1) For the first, maybe I need use an impulse conservation law:

v * L = M * u (u is the maximum speed of boat);

So:

u = v * L/ M

But can this be so simple?

Homework Statement

2) A comet flys to Earth with speed v. The angle between the speed vector and the straight, which connects Earth and the comet, is equal to alfa. What the value of speed v should be, that the comet:

a) would become a satellite of Earth;
b) would hit the Earth;
c) would escape from the gravitational influence of Earth;

Homework Equations

2) I have no idea about calculating these speeds :(. Is there enough data in the problem statement? Maybe the required speed depend on the distance between Earth and the comet.

Homework Statement

3)A heavy metal ball starts to fall from 1 meter height, ant this ball hits a light tennis-ball on the table. After the hit, metall ball rises nearly to 1 meter height. To what height does a light tennis-ball rise?

The Attempt at a Solution

An energy conservation law should be useful here. But then it means that a little tennis-ball rises to height which is nearly equal to zero.

Homework Statement

4) A dumbbell (distance between balls is l) stands upright on a flat. This dumbbell is released to move. What speed will have each ball when the dumbbell hits the flat (there is no friction).

The Attempt at a Solution

I think that there should energy conversation law and impulse moment
law be used.

As first, only the top ball and the stick between balls has got some potentional energy which is equal to

E1 = mgl + Mgl/2
m - mass of a ball;
M - mass of a stick;

When a dumbbell is released to move, it startes to turn around a ball which is on a flat. When a dumbbell hits a flat, all system has some kinetic energy:

Iw^2/2 - kinetic energy of a stic;

mv^2/2 - kinetic energy of a upper ball;

But I can't bring all these equations and ideas into one unit (I can't exclude the masses m and M from equations. Maybe a ball which is on flat also has got some kinetic energy when this system hits a flat, and the equation of kinetic energy of upper ball (mv^2/2) is different)

Thanks in advance.

 

[malawi_glenn]

to the comet question, i think you should express the velocity in terms of alpha.

 

[Petrulis]

to the comet question, i think you should express the velocity in terms of alpha.

I think the same way but I have now ideas about what formulas I should use here.

Kepler's laws doesn't look to be helpful in this case.