A block of 1.0 kg rests on the gap between two boards. Putty is throw from the underside of the block and makes contact with it. The Putty has a velocity of 15 m/s and weighs 0.3kg. Calculate the max height the block travels after contact with the putty, assuming they stick together.

To calculate the maximum height the block travels after contact with the putty, we can use the principle of conservation of momentum and the principle of conservation of energy.

1. Calculate the initial momentum of the putty:
Momentum = mass × velocity
In this case, the putty has a mass of 0.3 kg and a velocity of 15 m/s.
Initial momentum of the putty = 0.3 kg × 15 m/s

2. Calculate the initial momentum of the block (before the collision):
Since the block is initially at rest, its initial momentum is zero.

3. According to the principle of conservation of momentum, the total momentum before and after the collision is the same (assuming no external forces act on the system):
Initial momentum of the putty = Total momentum after collision

4. Calculate the final velocity of the block and putty (after the collision):
Final momentum of the block and putty = (Mass of block + Mass of putty) × Final velocity
In this case, the mass of the block is 1.0 kg and the mass of the putty is 0.3 kg.
Final momentum of the block and putty = (1.0 kg + 0.3 kg) × Final velocity

5. Equate the initial and final momenta and solve for the final velocity:
0.3 kg × 15 m/s = (1.0 kg + 0.3 kg) × Final velocity

6. Once you have the final velocity, you can calculate the maximum height the block achieves using the principle of conservation of energy:
The initial kinetic energy of the block and putty is equal to the potential energy at the maximum height.
Initial kinetic energy = 1/2 × (Mass of block + Mass of putty) × (Final velocity)^2
Potential energy at maximum height = (Mass of block + Mass of putty) × g × Height
Solve for the height:
1/2 × (1.0 kg + 0.3 kg) × (Final velocity)^2 = (1.0 kg + 0.3 kg) × 9.8 m/s^2 × Height

7. Rearrange the equation and solve for the maximum height:
Height = (1/2 × (1.0 kg + 0.3 kg) × (Final velocity)^2) / ((1.0 kg + 0.3 kg) × 9.8 m/s^2)

8. Substitute the value of the final velocity obtained in step 5 into the equation in step 7 to calculate the maximum height.

By following these steps, you should be able to calculate the maximum height the block travels after contact with the putty.