A 1.95-kg wooden block rests on a table over a large hole as in the figure below

Question

A 1.95-kg wooden block rests on a table over a large hole as in the figure below. A 5.70-g bullet with an initial velocity vi is fired upward into the bottom of the block and remains in the block after the collision. The block and bullet rise to a maximum height of 17.0 cm.

Calculate the initial velocity of the bullet from the information provided. (Let up be the positive direction.)

________ m/s

A 1.95-kg wooden block rests on a table over a large hole as in the figure below. A 5.70-g bullet with an initial velocity vi is fired upward into the bottom of the block and remains in the block after the collision. The block and bullet rise to a maximum height of 17.0 cm. Calculate the initial velocity of the bullet from the information provided. (Let up be the positive direction.) ________ m/s

Explanation / Answer

we can do this by working backwards...we know that the bullet block system has a final PE of

(M+m) gh and an initial KE of 1/2 (M+m)V^2 so that

V=speed of bullet/block = Sqrt[2 g h] = Sqrt[2x9.8m/s/s x 0.17m] = 1.825m/s

now we use conservation of momentum to find vi:

m vi = (M+m)V

vi=(1.9557kg x 1.825m/s)/0.0057kg = 626.167m/s

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