a bullet of 10g strikes a sand bag at a. speed. of 10�0…6m/s and gets embedded after traveling 5 cm. calculate

1) the resistive force exerted by sand on the bullet
2) the time taken by the bullet to come to rest

To calculate the resistive force exerted by the sand on the bullet:

Step 1: Find the initial kinetic energy of the bullet using the formula:

KE = 1/2 * m * v^2

Where:
KE = kinetic energy
m = mass of the bullet = 10g = 0.01kg
v = speed of the bullet = 10^6 m/s

KE = 0.5 * 0.01kg * (10^6 m/s)^2
KE = 0.5 * 0.01kg * 10^12 m^2/s^2
KE = 0.5 * 10^10 kg * m^2/s^2

Step 2: Find the work done by the resistive force using the formula:

W = force * distance

Where:
W = work done
force = resistive force exerted by the sand (unknown)
distance = 5 cm = 0.05m

The work done by the resistive force is equal to the initial kinetic energy of the bullet.

W = 0.5 * 10^10 kg * m^2/s^2

Step 3: Calculate the resistive force by rearranging the work formula:

force = W / distance

force = (0.5 * 10^10 kg * m^2/s^2) / 0.05m

Now we can calculate the resistive force exerted by the sand on the bullet.

To calculate the time taken by the bullet to come to rest:

Step 1: Use the formula of kinetic energy to find the final kinetic energy of the bullet, which is zero when it comes to rest.

KE = 1/2 * m * v^2

Where:
KE = kinetic energy (final = 0)
m = mass of the bullet = 10g = 0.01kg
v = final velocity of the bullet (unknown)

0 = 0.5 * 0.01kg * v^2

Rearrange the equation to solve for v:

v^2 = 0 / (0.5 * 0.01kg)
v^2 = 0

Step 2: Now we can calculate the time taken using the formula:

t = (change in velocity) / (acceleration)

Where:
t = time taken
change in velocity = final velocity - initial velocity = 0 - 10^6 m/s = -10^6 m/s (negative because it's opposing the initial velocity)
acceleration = force / mass
force = resistive force exerted by the sand (from previous calculation)
mass = mass of the bullet = 10g = 0.01kg

t = (-10^6 m/s) / (resistive force / 0.01kg)

Now we can calculate the time taken by the bullet to come to rest.

To calculate the resistive force exerted by the sand on the bullet, we can apply Newton's second law of motion. This law states that the net force acting on an object is equal to the product of its mass and acceleration.

1) The mass of the bullet is given as 10g, which can be converted to kilograms by dividing by 1000:
Mass = 10g ÷ 1000 = 0.01 kg

The initial velocity of the bullet is given as 10^6 m/s, and it comes to rest after traveling 5 cm (which can be converted to meters by dividing by 100):
Initial velocity (u) = 10^6 m/s
Distance (s) = 5 cm ÷ 100 = 0.05 m

We need to find the acceleration of the bullet to calculate the resistive force. We can use the equation of motion:
v^2 = u^2 + 2as
Rearranging the formula, we have:
a = (v^2 - u^2) / (2s)

Since the bullet comes to rest, the final velocity (v) is 0 m/s:
a = (0^2 - (10^6)^2) / (2 * 0.05)
a = -10^12 / 0.1
a = -10^13 m/s^2

Now, we can calculate the resistive force using Newton's second law:
F = ma
F = 0.01 kg * (-10^13 m/s^2)
F = -10^11 N

Therefore, the resistive force exerted by the sand on the bullet is -10^11 N (negative because it acts in the opposite direction of motion).

2) To calculate the time taken by the bullet to come to rest, we can use the equation:
v = u + at

Given that the final velocity (v) is 0 m/s and the initial velocity (u) is 10^6 m/s, the equation becomes:
0 = 10^6 m/s + (-10^13 m/s^2) * t

Solving for time (t):
10^13 m/s^2 * t = 10^6 m/s
t = (10^6 m/s) / (10^13 m/s^2)
t = 10^-7 s

Therefore, the time taken by the bullet to come to rest is 10^-7 seconds.

This makes no sense.

I don't know please help me