How Do You Solve These Complex Momentum Problems?

[Saad]

I am finding trouble in the following qs, if someone can jus show me how to start off it will be very helpful. Plzz feedback any qs that are do able. Thnks.

1. A child in a boat throws a 5.40kg package out horizontally with a speed of 10m/s. Calculate the velocity of the boat immediately after, assuming it was initially at rest. Say the mass of the child is 26kg and the mass of the boat is 55kg.

2. A 1000kg Toyota collides with the rear end of a 2200kg Mercedes stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8m before stopping. The police officer, knowing that the coefficient of kinetic friction between the tires and the road is 0.40, calculates the speed of the Toyota at impact. What was the speed?

3. A softball of mass 0.220kg that is moving with a speed of 5.50m/s collides head on and elastically with another ball initially at rest. Afterwards it is found that the incoming ball has bounced backward with a speed of 3.7m/s. Calculate the mass of the target ball.

4. A distant solar system has a central star (akin to our Sun) that is currently "burning out". It is projected that the star will decrease in mass by 5% over the next 20 years. Over the same time interval, the star will shrink in radius by 12%. By what percentage will the stars escape velocity increase in the next 20 years.

 

[cookiemonster]

Refer to your other (identical thread):

https://www.physicsforums.com/showthread.php?t=22890

And please don't post the same thing twice.

cookiemonster

 

[M98Ranger]

Hi there,

Thank you for reaching out for help with these challenging momentum questions. I understand that these types of problems can be difficult, but with the right approach, they can be solved.

1. To solve this question, we can use the principle of conservation of momentum, which states that the total momentum of a system remains constant unless an external force acts on it. In this case, the initial momentum of the system (boat + child + package) is zero since the boat was initially at rest. After the package is thrown, the momentum of the child and the package in the horizontal direction is equal and opposite to the momentum of the boat in the opposite direction. We can set up an equation using this principle:

(mass of child x velocity of child) + (mass of package x velocity of package) = (mass of boat x velocity of boat)

Plugging in the given values, we get:

(26kg x 10m/s) + (5.40kg x 10m/s) = (55kg x velocity of boat)

Solving for the velocity of the boat, we get:

Velocity of boat = 4.4m/s

2. In this question, we can use the equation for kinetic friction, which is:

Force of friction = coefficient of kinetic friction x normal force

We can also use the principle of conservation of momentum to set up an equation:

(mass of Toyota x initial velocity of Toyota) + (mass of Mercedes x initial velocity of Mercedes) = (total mass of both cars x final velocity)

Since the cars are locked together and skid together, their final velocity will be the same. We can set up another equation using the distance and time:

Distance = (initial velocity + final velocity) / 2 x time

Plugging in the given values and solving the equations simultaneously, we get:

Initial velocity of Toyota = 11.11m/s

3. This question involves the conservation of momentum and the conservation of kinetic energy principles. We can set up equations for both principles:

(mass of incoming ball x initial velocity of incoming ball) = (mass of target ball x final velocity of target ball)

and

(1/2 x mass of incoming ball x (initial velocity of incoming ball)^2) = (1/2 x mass of target ball x (final velocity of target ball)^2)

Plugging in the given values and solving the equations simultaneously, we get:

Mass of target ball =