A 0.0124-kg bullet is fired straight up at a falling wooden block that has a mass of 3.96 kg. The bullet has a speed of 756 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.

I solved for v and then using vf = vi + at i solved for t.
Is that correct?

Since the force of the bullet = the force of moving up

My guess:
set up two system of equations and solve for t?

(I am bookmarking this , great question)

I think it's a little more in depth than a system of eqns. :(

I think I got it. How did you find the acceleration of the bullet to plug into that equation?

To find the time t when the collision occurs, you need to consider the motion of the block and the bullet separately before the collision.

First, let's consider the motion of the block. It is initially dropped from rest, so its initial velocity is zero. Using the equation for free-fall motion, we can find the time it takes for the block to fall:

h = (1/2)gt^2

Where h is the height of the building, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time in seconds. Rearranging the equation to solve for t, we get:

t = sqrt(2h/g)

Next, let's consider the motion of the bullet. Since the bullet is being fired straight up, its initial velocity is 756 m/s (positive because it is going up). The bullet decelerates due to gravity until it comes to a stop at the top of the building. We can use the following equation to find the time it takes for the bullet to stop:

vf = vi - gt

Where vf is the final velocity (which is zero since the bullet stops), vi is the initial velocity of the bullet (756 m/s), g is the acceleration due to gravity (approximately -9.8 m/s^2, negative because it acts downward), and t is the time in seconds. Rearranging the equation to solve for t, we get:

t = vi / g

Now, we have the time it takes for the block to fall (t1) and the time it takes for the bullet to stop (t2). The time t we are looking for is the sum of these two times:

t = t1 + t2

To calculate this value, you need to know the height of the building. Plug in the values for h, vi, and g into the respective equations, and then add t1 and t2 to find the total time t.