Solve the following half-life problems. 1. The half-life of Pa-234 is 6.75 hr. How much (what fraction) of a sample of this isotope remains
after 20.25 hr?

2. The half-life of Rn-222 is 3.823 day. What was the original mass of a sample of this isotope if
0.0500 g remains after 7.646 day?

3. The half-life of Th-227 is 18.2 day. How many days are required for 0.70g of a given sample to
decay to 0.0875 g?

4. The half-life of carbon-14 is 5700 years. If a 10 gram sample undergoes decay for 17,100 years,
how many half-lives have the sample undergone?

    m₁v₁ + m₂v₂ = (m₁ + m₂)vmomentum is conserved.the left-hand side of the equation represents the momentum in the system before the collision.the right-hand side represents the momentum in the system after the collisionm₁ and v₁ represents the mass and the velocity of the physics blockm₂ and v₂ represents the mass and velocity of the ball of puttyv represents the final velocity of the combined mass.the question states the two masses stick together. they combined mass has its own velocity with the body mass the sum of the two objects' massestheir combined momentum is (m₁ + m₂)vto find the magitude of (m₁ + m₂)v, we need to add the vectors on the left-hand side of the equation: m₁v₁ + m₂v₂.note the diagram. i have positioned the vectors in accordance with their directions.the magnitude of the resultant can be calculated using the pythagorean theorem since this is a right triangle situation (north and west are perpendicular)|(m₁ + m₂)v| =  √[ (m₁v₁)² + (m₂v₂)² ]|(m₁ + m₂)v| =  √[ (1.5kg·8.0m/s)² + (0.40kg·20m/s)² ]|(m₁ + m₂)v| =  14.4 kg m/sfor two significant figures (assuming that 20m/s is two), this rounds to 14 kg m/s