A 2.50 g bullet, traveling at a speed of 435 m/s, strikes the wooden block of a ballistic pendulum, as shown. The block has a mass of 270 g.

(a) Find the speed of the bullet/block combination immediately after the collision.
m/s

(b) How high does the combination rise above its initial position?
m

To answer these questions, we can use the principle of conservation of momentum and conservation of mechanical energy.

(a) To find the speed of the bullet/block combination immediately after the collision, we need to first determine the final mass of the combination and then apply the principle of conservation of momentum.

1. Determine the final mass of the combination:
The bullet, initially weighing 2.50 g, becomes embedded in the block, which initially weighs 270 g. So the total mass of the combination after the collision is:
Total mass = mass of bullet + mass of block = 2.50 g + 270 g = 272.50 g = 0.27250 kg

2. Apply the principle of conservation of momentum:
The principle states that the total momentum before the collision is equal to the total momentum after the collision.
Initial momentum = final momentum

The initial momentum of the bullet is given by:
Initial momentum of bullet = mass of bullet × initial velocity of bullet
Initial momentum of bullet = 2.50 g × 435 m/s

The initial momentum of the block is zero, as it is initially at rest.

The final momentum of the combination is given by:
Final momentum of combination = total mass of combination × final velocity of combination

Setting the initial momentum equal to the final momentum, we have:
Initial momentum of bullet + initial momentum of block = Final momentum of combination
(2.50 g × 435 m/s) + (0 kg × 0 m/s) = (0.27250 kg × final velocity of combination)

Now we can solve for the final velocity of the combination.

(b) To find how high the combination rises above its initial position, we can use the principle of conservation of mechanical energy. The potential energy gained by the combination is equal to the initial kinetic energy of the combination.

1. Calculate the initial kinetic energy of the combination:
Initial kinetic energy = 1/2 × mass of combination × final velocity of combination^2
Initial kinetic energy = 1/2 × 0.27250 kg × (final velocity of combination)^2

2. Use the principle of conservation of mechanical energy:
The potential energy gained by the combination is equal to the initial kinetic energy.

Potential energy gained = mass of combination × acceleration due to gravity × height gained

Setting the initial kinetic energy equal to the potential energy gained, we can solve for the height gained by the combination.

Now, let's plug in the values and solve for the answers.