Physics block and bullet question

Question

To view an interactive solution to a problem that is similar to this one, select Interactive Solution 7.24. A 0.00579-kg bullet is fired straight up at a falling wooden block that has a mass of 1.54 kg. The bullet has a speed of 578 m/s when it strikes the block. The block originally was dropped from rest from the top of a building and had been falling for a time t when the collision with the bullet occurs. As a result of the collision, the block (with the bullet in it) reverses direction, rises, and comes to a momentary halt at the top of the building. Find the time t.

Answer 1

The acceleration due to gravity is the same on the block going down, as it is on the block and bullet going up. (Note that m does not appear in the kinematic equations of motion for constant acceleration.) Since the magnitude of the displacement is the same going up as it is going down, and the starting velocity on the way down is the same as the ending velocity on the way up, the final speed of the block on the way down must be the same as the initial speed on the way up, since::

|2g*delta y|=|(v_final)^2 -(v_initial)^2)|.

Therefore, the time it took to reach the top from where the block fell must be the same as the time it took to fall the same distance down.