Answer any one of them please!

1. A 12 kg block sliding at 6.5 m/s along a level floor encounters rough area where the coefficient of friction is 0.20. The rough area is 5 meters long. How fast will the block be moving as it leaves the rough area? Where did the energy go?

2. A 800 kg car traveling southward at 9.2 m/s collides with a 900 kg car traveling northward at 4.5 m/s.
The cars become entangled. What is the speed and direction of the cars immediately following the collision?

3. A 6kg block slides down a 2.0 m long frictionless ramp which is inclined 40 degrees above the ground.
a) find the height of the top of the ramp and then determine the speed at the bottom of the ramp.

b) If the block collides with, and sticks to a 8.2 kg block which had been at rest at the bottom of the ramp, how fast would they now move?

c) Determine how much energy the two blocks have after the collision.

You will need to post what you have tried to do to solve them though...

1.
Force due to friction is given by:

F = \mu R

where mu is the coefficient of friction, R is the normal reaction of the table on the mass. And remember that:

R = W = mg

Now, you have two possibilities, either use energy, or use kinematics.

Kinematics:
Use F = ma to find the acceleration of the block, then use v^2 = u^2 + 2as to get the speed with which the mass leaves the rough surface.

Energy:
Use W = Fd, then work out the kinetic energy of the mass, E_k = \frac12 mv^2, subtract the work done and use again the kinetic energy formula to get the final speed.

2. Use the principle of conservation of momentum.

m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2

3. (a) Make a sketch, and use trigonometry to find the height of the top of the ramp.

Since it's a frictionless ramp, working with energy is faster. Find the potential energy of the mass at the top of the ramp, then apply the principle of conservation of energy. At the bottom, use the kinetic energy to get the speed of the block.

(b) Use the equation of 2.

(c) Using your answer of (b), use the kinetic energy formula to get this.