Final answer:
To find the horizontal distance that the block covers before hitting the ground, calculate the time it takes for the block to reach the ground. Use the conservation of momentum to find the final velocity of the block and bullet system. Finally, calculate the horizontal distance using the final velocity and the time.
Step-by-step explanation:
To find the horizontal distance that the block covers before hitting the ground, we need to calculate the time it takes for the block to reach the ground.
First, use the conservation of momentum to find the final velocity of the block and bullet system. The initial momentum of the bullet is given by:
pi = mbvi
The final momentum of the system is given by:
pf = (mb + mblock)vf
Where mb is the mass of the bullet, mblock is the mass of the block, vi is the initial velocity of the bullet, and vf is the final velocity of the system.
Since the bullet embeds itself within the block, the final velocity of the system is zero. Therefore, we can set the initial and final momenta equal to each other and solve for the final velocity:
mbvi = (mb + mblock)vf
Solving for vf:
vf = (mbvi)/(mb + mblock)
With the final velocity of the system, we can calculate the time it takes for the block to reach the ground using the equation:
d = v0t + (1/2)at2
Where d is the vertical distance, v0 is the initial vertical velocity, t is the time, and a is the acceleration.
In this case, the initial vertical velocity is zero, since the block starts at rest. The vertical distance is given by the height of the table, and the acceleration is due to gravity (-9.8 m/s2). Rearranging the equation to solve for t:
t = sqrt((2d)/a)
Substituting the values, we find:
t = sqrt((2 * 0.790 m) / 9.8 m/s2)
Finally, we can calculate the horizontal distance using the equation:
d = vft
Substituting the values:
d = (vf) * sqrt((2 * 0.790 m) / 9.8 m/s2)
Calculating the result gives an horizontal distance of about 10.8 meters.