A 2-kg object moving to the right with a speed of 4 m/s makes a head-on, elastic collision with a 1-kg object that is initially at rest. The velocity of the 1-kg object after the collision is (a) greater than 4 m/s, (b) less than 4 m/s, (c) equal to 4 m/s, (d) zero, or (e) impossible to say based on the information provided.

To lift off from the Moon, a 9.50 105 kg rocket needs a thrust larger than the force of gravity. If the exhaust velocity is 4.25 103 m/s, at what rate does the exhaust need to be expelled to provide sufficient thrust? The acceleration due to gravity on the Moon is 1.62 m/s2.

(III) A 0.145-kg baseball pitched horizontally at 27.0 m/s strikes a bat and pops straight up to a height of 31.5 m. If the contact time between bat and ball is 2.5 ms, calculate the average force between the ball and bat during contact.

A rocket is fired vertically upward in a vaccum. During the burning process, the fuel mixture is expelled at a constant rate 1352 kg/s and the exhaust gas is ejected at a constant velocity with magnitude 523 m/s. (i) What percentage of the total initial mass M the rocket has to burn in order to accelerate to the speed of 605 m/s? (ii) What is the speed of rochet when 42% of its total initial mass M is ejected? (i) The rocket has to burn % of its total initial mass. Enter your answer to the nearest integer (whole number). (ii) The speed of the rocket ( relative to Earth) is equal to m/s. Enter your answer to the nearest m/s

2) (A)as shown in fig (1) ,m2 = 2 kg, h2 = 3 m ,ml = 4 kg, , hl = 0.95 m, and uk = 0.25. estimate (a) the velocity vl of mass ml as it hits the ground.(b) the kineticenergy of m1 h2

(3) This problem deals with a method for measuring the muzzle velocity of a rifle. A rifle with unknown muzzle velocity vo fires a bullet with mass m into a large block of wood with mass M that is sitting on a horizontal surface. The velocity of the block right after the (inelastic) collision is v. The block then slides a distance d along the surface and comes to a stop. The coefficient of kinetic friction between the block of wood and the surface is μk. (a) Use conservation of momentum (during the collision) and the work-energy theorem (after the collision) to show that the muzzle velocity of the rifle is given by: 20 = (m + M) √2 µx8d m (b) Calculate the muzzle velocity of the rifle if m= 5.00 g. M = 1.20 kg. d = 14.6 cm, and µ = 0.56. [answer: vo = 305 m/s]

(3) A bullet with mass 4.0 g and speed 650 m/s is fired at a block of wood with mass 0.095 kg. The block rests on a surface that is so slippery it can be considered frictionless and is thin enough so that the bullet passes completely through it. Immediately after the bullet exits the block, the speed of the block is 23 m/s. (a) What is the speed of the bullet when it exits the block? (answer: 100 m/s) (b) What percentage of the bullet's kinetic energy is lost during the collision (answer: 94.5%)

(II) Determine the fraction of kinetic energy lost by a neutron (m1 = 1.01 u) when it collides head-on and elastically with a target particle at rest which is (a) H (m = 1.01 u); (b) {H (heavy hydrogen, m = 2.01 u); (c) ?C (m = 12.00 u); (d) ²Pb (lead, m = 208 u). %D

(III) A bullet of mass m = 0.0010 kg embeds itself in a wooden block with mass M = 0.999 kg, which then com- presses a spring (k = 140 N/m) by a distance x = 0.050 m before coming to rest. The coefficient of kinetic friction between the block and table is M = 0.50. (a) What is the initial velocity (assumed horizontal) of the bullet? (b) What fraction of the bullet's initial kinetic energy is dissipated (in damage to the wooden block, rising temperature, etc.) %3D in the collision between the bullet and the block?