Question

An 8-kg block is hanging on a string when a .01 kg bullet is shot into it and gets stuck inside it from below. If the bullet and block rises to a height of 1.6m. What velocity did the bullet enter the block?

A. 1 m/s
B. 10 m/s
C. 100 m/s
D. 1000 m/s

Answer 1

Option C, 100 m/s.

The bullet's initial velocity as it enters the block can be calculated by equating the potential energy at the block's highest point to the bullet and block system's initial kinetic energy, yielding an answer of 100 m/s.

Step-by-step explanation:

To find out the velocity with which the bullet entered the block, we can use the principle of conservation of energy. Initially, the bullet has kinetic energy, which is partly converted into potential energy when the bullet and block system rises to a height of 1.6 meters. Using the formula for potential energy (PE) PE = mgh, where m is the mass of the system (bullet plus block), g is the acceleration due to gravity, and h is the height, we can calculate the initial kinetic energy (KE) of the system. Then, knowing that KE = ½mv² (where v is velocity), we can solve for v.

First, calculate the potential energy at 1.6 meters: PE = (8.01 kg)(9.8 m/s²)(1.6 m). Then, this equals the initial kinetic energy of the system: KE = ½(8.01 kg)(v²).

Solving this equation for v gives us the initial velocity of the bullet as it enters the block (assuming no energy is lost in the collision). After solving, we find the velocity to be Option C, 100 m/s.