a bullet of mass 10 gram is fired from a gun of mass 5 kg. If the gun recoils at the speed of 60m/s calculate the initial speed of the bullet.The bullet stops after penetrating 50 cm into a target. Find the opposing force to the motion of the bullet

a) mv (gun) = mv (bullet)

b) 1/2mv^2 = Fd
solve for f (and watch your units)

To calculate the initial speed of the bullet, we can use the principle of conservation of momentum. The momentum before the bullet is fired is equal to the momentum after.

The momentum of an object is given by the product of its mass and velocity.

Let's assume the initial velocity of the bullet is "v" m/s.

So, the initial momentum of the bullet will be:

Momentum of the bullet = mass of the bullet × initial velocity of the bullet
= (10 g) × v = 0.01 kg × v = 0.01v kg·m/s

The momentum of the gun will be:

Momentum of the gun = mass of the gun × recoil velocity of the gun
= (5 kg) × (60 m/s) = 300 kg·m/s

According to the conservation of momentum:

Momentum before = Momentum after

(0.01v) + (300) = 0 + 0

Simplifying the equation:

0.01v + 300 = 0
0.01v = -300
v = -300 / 0.01
v = -30,000 m/s

Since we are interested in the initial speed of the bullet, we consider the velocity to be positive in this case:

Initial speed of the bullet = |v| = |-30,000 m/s|
= 30,000 m/s

Therefore, the initial speed of the bullet is 30,000 m/s.

Now, to find the opposing force to the motion of the bullet, we can use the equation of motion:

force (F) = mass (m) × acceleration (a)

The acceleration of the bullet can be calculated using the formula:

acceleration (a) = (final velocity)^2 - (initial velocity)^2 / (2 × distance)

Given:
Final velocity (vf) = 0 m/s (since the bullet stops)
Initial velocity (vi) = 30,000 m/s (as calculated above)
Distance (d) = 50 cm = 0.5 m

Using the formula:

a = (0^2 - 30,000^2) / (2 × 0.5)
= -900,000,000 / 1
= -900,000,000 m/s^2

Since acceleration is a vector quantity, the negative sign indicates the direction opposite to the motion of the bullet.

Now, we can calculate the opposing force (F) using the equation:

F = m × a

Substituting the values:

F = 0.01 kg × (-900,000,000 m/s^2)
= -9,000,000 N

Therefore, the opposing force to the motion of the bullet is 9,000,000 Newtons (N) in the opposite direction.