a 20-g projectile strikes a mud bank penetrating a distance of 6 cm before stopping. find the stopping force F if the entrance velocity is 80 meter per second.

same as last one

F * d = (1/2) m v^2

D * .06 = (1/2) *.020 * 6400

Am not comfortable with the work I mean show full working thanks

To find the stopping force (F), we can use the equation of motion:

F = (mv^2) / (2d)

where:
F = stopping force
m = mass of the projectile (20 g = 0.02 kg)
v = entrance velocity (80 m/s)
d = distance penetrated (6 cm = 0.06 m)

Substituting the given values into the equation, we get:

F = (0.02 kg * (80 m/s)^2) / (2 * 0.06 m)

Calculating the equation, we have:

F = (0.02 kg * 6400 m^2/s^2) / (0.12 m)
F = 128 N

Therefore, the stopping force (F) is 128 Newtons.

To find the stopping force F, we can use the equation for impulse.

The impulse of an object can be calculated using the equation:

Impulse = Change in momentum

The change in momentum can be calculated using the equation:

Change in momentum = Final momentum - Initial momentum

In this case, the initial momentum is given by the mass of the projectile multiplied by the initial velocity:

Initial momentum = mass × initial velocity

The final momentum is given by the mass of the projectile multiplied by the final velocity, which in this case is zero since the projectile stops:

Final momentum = mass × final velocity

Since the final velocity is zero:

Final momentum = 0

The change in momentum is therefore:

Change in momentum = 0 - (mass × initial velocity)
= -mass × initial velocity

Now, let's rearrange the equation for impulse to solve for the stopping force F:

Impulse = Change in momentum

Impulse = Force × time

Rearranging the equation:

Force = Impulse / time

In this case, we need to find the stopping force F, so we rearrange the equation and solve for F:

F = Impulse / time

However, we don't know the time it takes for the projectile to stop. To find the time, we need to use the equation for average speed:

Average speed = distance / time

In this case, the average speed is the initial velocity. Therefore:

Average speed = initial velocity

Rearranging the equation:

time = distance / average speed

Now, we have all the components we need to find the stopping force F.

First, let's calculate the change in momentum using the mass and initial velocity given:

Change in momentum = -mass × initial velocity

Next, calculate the time it takes for the projectile to stop using the given distance and initial velocity:

time = distance / average speed
= 6 cm / (80 m/s)
= 0.06 m / (80 m/s)
= 0.00075 s

Finally, substitute the values into the equation to find the stopping force F:

F = Change in momentum / time
= (-mass × initial velocity) / time

Note: You need to provide the mass of the projectile to calculate the stopping force accurately.