need help on this three part one

its about inelastic collisions momentum and energy related with work

Find the speed at which Superman (mass=76.0 kg) must fly into a train (mass = 17620 kg) traveling at 60.0 km/hr to stop it.

Running into the train at that speed would severely damage both train and passengers. Calculate the minimum time Superman must take to stop the train, if the passengers experience an average horizontal force of 0.430 their own weight.

How far does the train then travel while being slowed to a stop?

first, use conservation of momentum to find superman must fly.

Second, use impulse=change of momentum
You are given the average force.

averageforce*time=weight/g *velocity
.43avgweight*tim=avgweigh/g *velocity
solve for time

Lastly, the average velocity stopping is 30km/hr, you know the time, so solve for distance.

first part:

Pi=Pf
Pf=0 (train is not moving)
0= m1v1 + m2v2
v2=m1v1/m2

To solve this three-part problem, we need to apply the principles of momentum, energy, work, and kinematics. Let's break it down step by step.

Part 1: Find the speed at which Superman must fly into a train to stop it.

In an inelastic collision, the momentum is conserved, but the kinetic energy is not. Let's denote the initial velocity of the train as v1, final velocity as v2, and the velocity of Superman as v.

The momentum of the system before the collision is equal to the momentum after the collision:

(mass of Superman * v) + (mass of train * v1) = (mass of Superman + mass of train) * v2

Plugging in the given values:

(76.0 kg * v) + (17620 kg * 60.0 km/hr) = (76.0 kg + 17620 kg) * 0

Convert the given velocity to m/s: 60.0 km/hr = (60.0 * 1000) / 3600 = 16.67 m/s

(76.0 kg * v) + (17620 kg * 16.67 m/s) = (76.0 kg + 17620 kg) * 0

Now we solve this equation to find the value of v:

(76.0 kg * v) = - (17620 kg * 16.67 m/s)

v = - (17620 kg * 16.67 m/s) / 76.0 kg

v ≈ -3850.8 m/s

The negative sign indicates that Superman needs to fly in the opposite direction to stop the train.

Therefore, Superman needs to fly at a speed of approximately 3850.8 m/s in the opposite direction to stop the train.

Part 2: Calculate the minimum time Superman must take to stop the train if the passengers experience an average horizontal force of 0.430 their own weight.

To find the time, we need to calculate the acceleration experienced by Superman. We can use Newton's second law, F = ma, where F is the force, m is the mass, and a is the acceleration.

We know that F = 0.430 * weight of the passengers.

Since the weight of the passengers is equal to the force of gravity acting on them, we can write:

weight of the passengers = mass of the passengers * gravitational acceleration

The average horizontal force experienced by passengers is given as 0.430 times their own weight, so we have:

F = 0.430 * (mass of the passengers * gravitational acceleration)

Now, using Newton's second law:

0.430 * (mass of the passengers * gravitational acceleration) = mass of Superman * acceleration

We know the mass of Superman, which is 76.0 kg, so we can solve for the acceleration:

acceleration = (0.430 * (mass of the passengers * gravitational acceleration)) / (mass of Superman)

Next, we can use the kinematic equation v = u + at, where v is the final velocity (0 m/s), u is the initial velocity (3850.8 m/s), acceleration is the value we just calculated, and t is the time taken to stop the train.

Now, we can solve the equation for t:

0 = 3850.8 m/s + (acceleration) * t

By substituting the calculated values and solving for t, we can find the minimum time Superman must take to stop the train.

Part 3: Calculate how far the train travels while being slowed to a stop.

To calculate how far the train travels while being slowed to a stop, we need to use the equation of motion:

s = ut + (1/2)at^2

In this equation, s represents displacement, u is the initial velocity of the train, a is the acceleration, and t is the time taken to stop the train.

Substituting the values we know:

s = (initial velocity of the train) * t + (1/2) * (acceleration) * t^2

Once we have determined the time taken to stop the train from Part 2, we can plug that value into the equation along with the initial velocity of the train to calculate the distance the train travels while being slowed to a stop.

Do note that the calculations require specific numerical values for the masses, velocities, and acceleration involved, as provided in the question.