Physics Problem Solving: Momentum, Energy, and Forces

1. How fast was the bullet moving when it left the barrel? 2. How fast is the wheel moving when leaving the ramp? 3. How far from the right end should Kelly be in order to drop the zombie? 4. How long should Kelly keep her eyes closed while running towards the zombie? 1. The speed of the bullet when it left the barrel can be calculated using the principle of conservation of momentum. The momentum of the bullet before the collision is 0.05v kg·m/s, where v is the velocity of the bullet. This momentum is equal to the momentum of the block and bullet after the collision, which is 5.05 kg·m/s. By solving these equations, we can determine the speed of the bullet. 2. To find the speed of the wheel when leaving the ramp, we can utilize the principle of conservation of mechanical energy. By comparing the initial mechanical energy at the top of the hill with the final mechanical energy at the bottom of the ramp, we can calculate the speed of the wheel. 3. Using Newton's second law of motion, we can calculate the acceleration of the platform and determine the force exerted by Kelly to drop the zombie. This allows us to find the distance from the right end that Kelly needs to be to achieve this. 4. By knowing Kelly's mass and the force she exerts to reach a specific velocity, we can calculate the time she should keep her eyes closed while running towards the zombie.

1. Bullet and Block Collision

a. Speed of the Bullet: The speed of the bullet when it left the barrel can be found by equating the momentum before and after the collision. The momentum of the bullet before the collision is 0.05v kg·m/s, and after the collision, it combines with the block to have a momentum of 5.05 kg·m/s. By solving the equation 0.05v = 5.05, we get the speed of the bullet.

b. Spring Period: The period of the spring can be calculated using the formula period = 2π * sqrt(mass / spring constant). Substituting the given values, we can find the period of the spring in motion.

c. Spring Position Equation: The equation for the position of the spring oscillator can be expressed as x = A * cos(2π * t / T), where x is the displacement, A is the amplitude (compression of the spring), t is the time, and T is the period of the spring.

2. Tractor Wheel Movement

a. Speed Leaving the Ramp: Utilizing the conservation of mechanical energy, we can determine the speed of the wheel when leaving the ramp by comparing initial and final mechanical energies.

b. Altitude Achieved: By setting the initial and final mechanical energies equal, we can calculate the altitude the wheel reaches during its movement.

3. Kelly and the Zombie Scenario

a. Dropping the Zombie: Kelly needs to calculate the acceleration of the platform to determine the force she exerts to drop the zombie. By applying Newton's second law of motion, she can find the distance from the right end she should be to achieve this.

b. Eyes Closed Duration: With knowledge of Kelly's mass and the force she exerts to reach a specific velocity, the time she should keep her eyes closed while running towards the zombie can be calculated.

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