A 17.5 g bullet is shot directly into a 3.55 kg block of wood which is at rest
on a table. The coefficient of friction between the block and the table is
0.358 and it slides a total of 1.14 m before coming to rest. What is the
muzzle velocity of the gun used to fire the bullet?

The muzzle velocity of the gun with which the bullet is fired is 40.2 m/s.

Explanation:

Muzzle velocity is defined as the speed at which the bullet pierces the target. So in order to find that we need the acceleration at which the bullet is travelling.

As here the mass of the target which is the wooden block is given and also the coefficient of friction between the block and table is given.

So from these two parameters , the force acting on the wood block can be determined as follows.

Force = coefficient of friction × Normal force

Force = -0.358×3.55×9.8= -12.45 N

So for this frictional force generation, the bullet targeting the block should be proportional acceleration. So from Newton's second law of motion,

F = Mass × acceleration

As the mass of the bullet is 17. 5 g and the force generated due to this mass is frictional force which is equal to 12.45 N.

Then acceleration = Force /Mass

Acceleration =-

Acceleration = -711 m/s².

So with this acceleration, the gun crosses a distance of 1.14 m in the wooden block before coming to rest. So the initial velocity of the bullet can be determined using second law of motion.

Here the final velocity v = 0, initial velocity we have to determine, acceleration a = 711 m/s² and displacement s = 1.14 m.

u² = 1621

u = 40.2 m/s

So the muzzle velocity of the gun with which the bullet is fired is 40.2 m/s.

the bal will not change its velocity.