How Fast Was the Bullet Going Initially?

[dcangulo]

A 2.0 kg block of wood rests on a tabletop. A 7.0 kg bullet is shot straight up through a hole in the table beneath the block. The bullet lodges in the block, and the block flies 25 cm above the tabletop. How fast was the bullet going initially?

i tried using this formula:
p= [m$$_{}b$$/(m$$_{}w$$(sin90))]v$$_{}b$$

but it doesn't give me the velocity of anything
maybe I am using the wrong the formula for this?
does the 25cm play a part in anything??

 

[rl.bhat]

Using kinematic equation, find the initial velocity of block and bullet to reach a height 25 cm above table top. Then applying the conservation linear momentum find the velocity of the bullet.

 

[nlightner]

Hello,

Thank you for sharing your attempt at using the formula for linear momentum. However, the formula you used is not applicable in this scenario as it is for calculating the final momentum of an object after a collision.

To find the initial velocity of the bullet, we can use the conservation of momentum principle, which states that the total momentum of a system remains constant before and after a collision. In this case, the system consists of the block and the bullet.

We can express this principle mathematically as follows:

Initial momentum of the system = final momentum of the system

The initial momentum of the system can be calculated as the sum of the individual momenta of the block and the bullet before the collision. The final momentum of the system can be calculated as the sum of the individual momenta of the block and the bullet after the collision.

Since the bullet is shot straight up, its initial horizontal velocity is zero. Therefore, we can ignore the horizontal component of its momentum and only consider the vertical component.

Initial momentum of the system = (mass of bullet)(initial vertical velocity of bullet) + (mass of block)(initial vertical velocity of block)

Final momentum of the system = (mass of bullet)(final vertical velocity of bullet + (mass of block)(final vertical velocity of block)

Since the bullet lodges in the block, the final vertical velocity of the bullet and the block is the same. We can also assume that the block moves with a constant velocity after the collision.

Therefore, we can write the equation as:

(mass of bullet)(initial vertical velocity of bullet) = (mass of bullet + mass of block)(final vertical velocity of bullet)

Solving for the initial velocity of the bullet, we get:

Initial velocity of bullet = [(mass of bullet + mass of block)(final vertical velocity of bullet)] / (mass of bullet)

Substituting the given values, we get:

Initial velocity of bullet = [(7.0 kg + 2.0 kg)(0.25 m/s)] / (7.0 kg)

= 0.0357 m/s

Therefore, the initial velocity of the bullet was approximately 0.0357 m/s.

The 25 cm distance does not play a direct role in calculating the initial velocity of the bullet. However, it is important in determining the vertical displacement of the block after the collision. This information can be used to calculate other quantities such as the kinetic energy and momentum of the system.

I hope