Solving Physics Problems: Finding Speed and Displacement

[dronegun]

i am finding these hard. Any help appreciated

A 1.0 103 kg Rover collides into the rear end of a 2.2 103 kg BMW stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.1 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.36, calculates the speed of the Rover at impact. What was that speed?

A 16 g rifle bullet traveling 235 m/s buries itself in a 3.1 kg pendulum hanging on a 2.8 m long string, which makes the pendulum swing upward in an arc. Determine the horizontal component of the pendulum's displacement.

A 0.200 kg croquet ball makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?
kg
(b) What fraction of the original kinetic energy (KE/KE) gets transferred to the second ball?

 

[AlephZero]

You need to use two principles, conservation of momentum, and conservation of energy.

Remember momentum is conserved when the impact occurs, but energy is not.

For the first question, call the velocity before the impact V1 and after the impact V2. So you need two equations to find two unknowns. First equation: After the impact, the kinetic energy of the cars = the work done by friction of the tires. Second equation: During the impact, momentum is concerved.

 

[kyle8921]

I understand that solving physics problems can be challenging, but with practice and understanding of the concepts, it can become easier. Speed and displacement are fundamental concepts in physics and can be solved using the equations of motion and conservation of energy.

In the first problem, we can use the equation v^2 = u^2 + 2as to find the speed of the Rover at impact. Here, v is the final velocity (0 m/s since both cars come to a stop), u is the initial velocity (which we need to find), a is the acceleration (which we can find using the coefficient of kinetic friction and the weight of the cars), and s is the displacement (2.1 m). By plugging in the given values, we can solve for u and find the speed of the Rover at impact.

In the second problem, we can use the principle of conservation of momentum to find the horizontal component of the pendulum's displacement. We know that the momentum of the bullet before and after the collision should be equal, and we can use this to find the velocity of the pendulum after the collision. From there, we can use the equation s = ut + 1/2 at^2 to find the horizontal displacement of the pendulum.

In the third problem, we can use the principle of conservation of kinetic energy to find the mass of the second ball and the fraction of kinetic energy transferred. We know that the total kinetic energy before and after the collision should be equal, and we can use this to find the mass of the second ball. From there, we can use the equation KE = 1/2 mv^2 to find the fraction of kinetic energy transferred to the second ball.

I hope this helps in understanding how to approach and solve these types of problems. Remember to always pay attention to the given information, use the relevant equations, and check your units and calculations. With practice and perseverance, you can master solving physics problems.