An 8.07g bullet is fired into a 340g block that is initially at rest at the edge

Question

An 8.07g bullet is fired into a 340g block that is initially at rest at the edge of a frictionless table of height h = 1.03 m (see the figure below).

The bullet remains in the block, and after the impact the block lands d = 2.07 m from the bottom of the table. How much time does it take the block to reach the ground once it flies off the edge of the table?

What is the initial horizontal velocity of the block as it flies off the table? (assume this to be in the positive direction)

Determine the initial speed of the bullet.

Explanation / Answer

h = ut + at^2 /2

1.03 = 0 + 9.81 t^2 /2

t = 0.458 sec

u   = d/t   = 4.52 m/s

using momnetum conservation,

8.07 x u1 = (8.07 +340) x 4.52

u1 = 194.83 m/s

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