A bullet of 10g enters a target at 100 ms-1 and leaves it 0.01 s later. Calculate:

i. The rate of change of momentum of the bullet
ii. The resistance offered by the target
iii. The loss of kinetic energy of the bullet
iv. The deceleration of the bullet
v. The distance travelled by the bullet in passing through the target

To calculate the various quantities related to the bullet entering and leaving the target, we can make use of the principles of physics. Let's go through each question step by step:

i. The rate of change of momentum of the bullet:
The rate of change of momentum is given by the equation:
Rate of change of momentum = (Final momentum - Initial momentum) / Time

We are given the mass of the bullet (10g), the initial velocity (100 ms^-1), and the time (0.01s). The momentum of an object is given by the equation:
Momentum = mass * velocity

So, we need to calculate the final momentum first. The mass remains the same, but the velocity changes as the bullet enters and leaves the target. Assuming no external forces act on the bullet, the final momentum will be equal to the initial momentum.

Therefore, the rate of change of momentum is 0, since the final momentum equals the initial momentum.

ii. The resistance offered by the target:
The resistance offered by the target is equal to the force applied by the target on the bullet to bring it to rest. This force is equal to the rate of change of momentum, which we just calculated to be 0 in this case. Hence, the resistance offered by the target is also 0.

iii. The loss of kinetic energy of the bullet:
The loss of kinetic energy of the bullet can be calculated using the equation:
Loss of kinetic energy = Initial kinetic energy - Final kinetic energy

The initial kinetic energy of the bullet is given by the equation:
Initial kinetic energy = 0.5 * mass * (initial velocity)^2

The final kinetic energy is given by:
Final kinetic energy = 0.5 * mass * (final velocity)^2

Since the bullet comes to rest, the final velocity is 0. Substituting these values into the equation, we get:
Loss of kinetic energy = 0.5 * mass * (initial velocity)^2

iv. The deceleration of the bullet:
The deceleration of an object is given by the equation:
Deceleration = (Final velocity - Initial velocity) / Time

Once again, assuming no external forces act on the bullet, the final velocity will be 0. Substituting the values into the equation, we get:
Deceleration = (0 - 100) / 0.01

v. The distance travelled by the bullet in passing through the target:
The distance traveled by the bullet can be calculated using the equation:
Distance = Initial velocity * Time

Substituting the given values into the equation, we get:
Distance = 100 * 0.01

Now, let's compute the specific values for each question:
i. The rate of change of momentum of the bullet is 0.
ii. The resistance offered by the target is 0.
iii. The loss of kinetic energy of the bullet is 0.5 * 0.01 * (100)^2 = 50 J.
iv. The deceleration of the bullet is (0 - 100) / 0.01 = -10,000 ms^-2.
v. The distance traveled by the bullet in passing through the target is 100 * 0.01 = 1 meter.

Please note that these calculations assume ideal conditions and neglect the effects of air resistance and other external factors.