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A bullet of mass m is moving horizontally with speed
A bullet of mass m is moving horizontally with speedvo when it hits a block of mass 100m that is at rest on a
horizontal frictionless table, as shown. The surface of the
table is a height h above the floor. After the impact, the
bullet and the block slide off the table and hit the floor a
distance x from the edge of the table. Derive expressions
for the following quantities in terms of m. h. vo, and
appropriate constants: (a) the speed of the block as it
leaves the table, (b) the change in kinetic energy of the
bullet-block system during impact, and (c) x.
Suppose that the bullet passes through the block instead of
remaining in it. (d) State whether the time required for the
block to reach the floor from the edge of the table would
now be greater, less, or the same. Justify your answer.
(e) State whether the distance x for the block would now be
greater, less, or the same. Justify your answer.
The speed of the block as it leaves the table is vo / 101, the change in kinetic energy can be calculated using initial and final kinetic energies, and the distance x is derived from projectile motion equations.The question involves a collision between a bullet of mass m and a block of mass 100m on a frictionless table. The following expressions are derived:The speed of the block as it leaves the table, assuming a perfectly inelastic collision, is given by vblock = vo / 101.The change in kinetic energy (ΔKE) of the bullet-block system during impact can be calculated using KE initial - KE final, where KE initial is ½mvo² and KE final is ½(101m)(vo/101)².The distance x is derived from projectile motion equations, x = vblock * sqrt((2h)/g), where g is the acceleration due to gravity.For parts (d) and (e), where the bullet passes through the block:The time for the block to reach the floor remains the same, as it is dependent only on the height h and gravity g.The distance x for the block would now be less because the block would have a lower horizontal velocity after being struck by the bullet....